This document defines and explains various types of regression analysis including linear, logistic, polynomial, stepwise, ridge and lasso regression. It discusses the key differences between correlation and regression. It also covers topics such as the least squares method, R-squared/coefficient of determination, adjusted R-squared, limitations of regression analysis and applications of regression analysis.
Regression analysis is a statistical technique for investigating relationships between variables. Simple linear regression defines a relationship between two variables (X and Y) using a best-fit straight line. Multiple regression extends this to model relationships between a dependent variable Y and multiple independent variables (X1, X2, etc.). Regression coefficients are estimated to define the regression equation, and R-squared and the standard error can be used to assess the goodness of fit of the regression model to the data. Regression analysis has applications in pharmaceutical experimentation such as analyzing standard curves for drug analysis.
Regression analysis is a statistical technique used to estimate the relationships between variables. It allows one to predict the value of a dependent variable based on the value of one or more independent variables. The document discusses simple linear regression, where there is one independent variable, as well as multiple linear regression which involves two or more independent variables. Examples of linear relationships that can be modeled using regression analysis include price vs. quantity, sales vs. advertising, and crop yield vs. fertilizer usage. The key methods for performing regression analysis covered in the document are least squares regression and regressions based on deviations from the mean.
Regression analysis is a statistical technique for predicting a dependent variable based on one or more independent variables. Simple linear regression fits a straight line to the data to predict a continuous dependent variable (y) from a single independent variable (x). The output is an equation of the form y= b0 + b1x + ε, where b0 is the y-intercept, b1 is the slope, and ε is the error. Multiple linear regression extends this to include more than one independent variable. Regression analysis calculates the "best fit" line that minimizes the residuals, or differences between predicted and observed y values.
- Regression analysis is a statistical tool used to examine relationships between variables and can help predict future outcomes. It allows one to assess how the value of a dependent variable changes as the value of an independent variable is varied.
- Simple linear regression involves one independent variable, while multiple regression can include any number of independent variables. Regression analysis outputs include coefficients, residuals, and measures of fit like the R-squared value.
- An example uses home size and price data from 10 houses to generate a linear regression equation predicting that price increases by around $110 for each additional square foot. This model explains 58% of the variation in home prices.
Multiple regression analysis allows researchers to examine the relationship between one dependent or outcome variable and two or more independent or predictor variables. It extends simple linear regression to model more complex relationships. Stepwise regression is a technique that automates the process of building regression models by sequentially adding or removing variables based on statistical criteria. It begins with no variables in the model and adds variables one at a time based on their contribution to the model until none improve it significantly.
Regression analysis is a statistical technique used to investigate relationships between variables. It allows one to determine the strength of the relationship between a dependent variable (usually denoted by Y) and one or more independent variables (denoted by X). Multiple regression extends this to analyze the relationship between a dependent variable and multiple independent variables. The goals of regression analysis are to understand how the dependent variable changes with the independent variables and to use the independent variables to predict the value of the dependent variable. It requires the dependent variable to be continuous and the independent variables can be either continuous or categorical.
This document discusses multiple linear regression analysis. It begins by defining a multiple regression equation that describes the relationship between a response variable and two or more explanatory variables. It notes that multiple regression allows prediction of a response using more than one predictor variable. The document outlines key elements of multiple regression including visualization of relationships, statistical significance testing, and evaluating model fit. It provides examples of interpreting multiple regression output and using the technique to predict outcomes.
Multiple regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of two or more variables.
Regression analysis is a statistical technique for investigating relationships between variables. Simple linear regression defines a relationship between two variables (X and Y) using a best-fit straight line. Multiple regression extends this to model relationships between a dependent variable Y and multiple independent variables (X1, X2, etc.). Regression coefficients are estimated to define the regression equation, and R-squared and the standard error can be used to assess the goodness of fit of the regression model to the data. Regression analysis has applications in pharmaceutical experimentation such as analyzing standard curves for drug analysis.
Regression analysis is a statistical technique used to estimate the relationships between variables. It allows one to predict the value of a dependent variable based on the value of one or more independent variables. The document discusses simple linear regression, where there is one independent variable, as well as multiple linear regression which involves two or more independent variables. Examples of linear relationships that can be modeled using regression analysis include price vs. quantity, sales vs. advertising, and crop yield vs. fertilizer usage. The key methods for performing regression analysis covered in the document are least squares regression and regressions based on deviations from the mean.
Regression analysis is a statistical technique for predicting a dependent variable based on one or more independent variables. Simple linear regression fits a straight line to the data to predict a continuous dependent variable (y) from a single independent variable (x). The output is an equation of the form y= b0 + b1x + ε, where b0 is the y-intercept, b1 is the slope, and ε is the error. Multiple linear regression extends this to include more than one independent variable. Regression analysis calculates the "best fit" line that minimizes the residuals, or differences between predicted and observed y values.
- Regression analysis is a statistical tool used to examine relationships between variables and can help predict future outcomes. It allows one to assess how the value of a dependent variable changes as the value of an independent variable is varied.
- Simple linear regression involves one independent variable, while multiple regression can include any number of independent variables. Regression analysis outputs include coefficients, residuals, and measures of fit like the R-squared value.
- An example uses home size and price data from 10 houses to generate a linear regression equation predicting that price increases by around $110 for each additional square foot. This model explains 58% of the variation in home prices.
Multiple regression analysis allows researchers to examine the relationship between one dependent or outcome variable and two or more independent or predictor variables. It extends simple linear regression to model more complex relationships. Stepwise regression is a technique that automates the process of building regression models by sequentially adding or removing variables based on statistical criteria. It begins with no variables in the model and adds variables one at a time based on their contribution to the model until none improve it significantly.
Regression analysis is a statistical technique used to investigate relationships between variables. It allows one to determine the strength of the relationship between a dependent variable (usually denoted by Y) and one or more independent variables (denoted by X). Multiple regression extends this to analyze the relationship between a dependent variable and multiple independent variables. The goals of regression analysis are to understand how the dependent variable changes with the independent variables and to use the independent variables to predict the value of the dependent variable. It requires the dependent variable to be continuous and the independent variables can be either continuous or categorical.
This document discusses multiple linear regression analysis. It begins by defining a multiple regression equation that describes the relationship between a response variable and two or more explanatory variables. It notes that multiple regression allows prediction of a response using more than one predictor variable. The document outlines key elements of multiple regression including visualization of relationships, statistical significance testing, and evaluating model fit. It provides examples of interpreting multiple regression output and using the technique to predict outcomes.
Multiple regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of two or more variables.
The document discusses simple linear regression analysis. It provides definitions and formulas for simple linear regression, including that the regression equation is y = a + bx. An example is shown of using the stepwise method to determine if there is a significant relationship between number of absences (x) and grades (y) for students. The analysis finds a significant negative relationship, meaning more absences correlated with lower grades. Formulas are provided for calculating the slope, intercept, and testing significance of the regression model.
Regression Analysis is simplified in this presentation. Starting with simple linear to multiple regression analysis, it covers all the statistics and interpretation of various diagnostic plots. Besides, how to verify regression assumptions and some advance concepts of choosing best models makes the slides more useful SAS program codes of two examples are also included.
Regression analysis measures the average relationship between two or more variables using their original data units. There are two main types: simple regression involving two variables, and multiple regression involving more than two variables. Regression can be linear, following a straight line, or non-linear/curvilinear. A simple linear regression model relates a dependent variable Y to an independent variable X plus an error term. Estimating the model involves calculating the slope/regression coefficient and intercept. Multiple regression relates a dependent variable to two or more independent variables using a multiple correlation coefficient.
Here are the key steps and results:
1. Load the data and run a multiple linear regression with x1 as the target and x2, x3 as predictors.
R-squared is 0.89
2. Add x4, x5 as additional predictors.
R-squared increases to 0.94
3. Add x6, x7 as additional predictors.
R-squared further increases to 0.98
So as more predictors are added, the R-squared value increases, indicating more of the variation in x1 is explained by the model. However, adding too many predictors can lead to overfitting.
The document discusses regression and correlation analysis. It defines regression analysis as estimating the values of one variable from knowledge of another variable. Correlation analysis measures the strength of association between variables. Regression analysis can be linear, exponential, logarithmic or power. Linear regression finds the best-fit straight line to describe the relationship between two variables. The correlation coefficient measures the extent of correlation between -1 and 1. Values above the critical t-value indicate a significant correlation. Examples are provided to demonstrate calculating the linear regression equation and correlation coefficient.
Through this ppt you could learn what is Wilcoxon Signed Ranked Test. This will teach you the condition and criteria where it can be run and the way to use the test.
The document discusses a one-way ANOVA test, which compares the means of two or more independent groups on a continuous dependent variable. It outlines the assumptions of the test, how to set it up in SPSS, and how to interpret the output. Key outputs include an ANOVA table showing if group means are statistically significantly different, and a post-hoc test for determining the nature of differences between specific groups.
Mpc 006 - 02-03 partial and multiple correlationVasant Kothari
3.2 Partial Correlation (rp)
3.2.1 Formula and Example
3.2.2 Alternative Use of Partial Correlation
3.3 Linear Regression
3.4 Part Correlation (Semipartial correlation) rsp
3.4.1 Semipartial Correlation: Alternative Understanding
3.5 Multiple Correlation Coefficient (R)
The Statistical Inference is the process of drawing conclusions about on underlying population based on a sample or subset of the data.
In most cases, it is not practical to obtain all the measurements in a given population.
The statistical inference is deals with decision problems. There are two types of decision problems as mentioned below:
(i) Problems of estimation and
(ii) Test of hypotheses
In the problem of estimation, we must determine the value of parameter(s), while in test of hypothesis we must decide whether to accept or reject a specific value(s) of a parameter(s).
This document discusses hypothesis testing and the t-test. It covers:
1) The basics of hypothesis testing including null and alternative hypotheses, types of hypotheses, and types of errors.
2) The t-test, which is used for small samples from a normally distributed population. It relies on the t-distribution and the degree of freedom.
3) Applications of the t-test including testing the significance of a single mean, difference between two means, and paired t-tests.
4) When sample sizes are large, the normal distribution can be used instead in Z-tests for similar applications.
The document discusses hypothesis testing and provides examples to illustrate the process. It explains how to state the research question and hypotheses, set the decision rule, calculate test statistics, decide if results are significant, and interpret the findings. An example tests if narcissistic individuals look in the mirror more often than others and finds they do based on a test statistic exceeding the critical value. A second example finds no significant difference in recovery time for patients with or without social support after surgery.
Correlation & Regression Analysis using SPSSParag Shah
Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
- Regression analysis is a statistical technique for modeling relationships between variables, where one variable is dependent on the others. It allows predicting the average value of the dependent variable based on the independent variables.
- The key assumptions of regression models are that the error terms are normally distributed with zero mean and constant variance, and are independent of each other.
- Linear regression specifies that the dependent variable is a linear combination of the parameters, though the independent variables need not be linearly related. In simple linear regression with one independent variable, the least squares estimates of the intercept and slope are calculated to minimize the sum of squared errors.
Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six –Sigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
This presentation educates you about T-Test, Key takeways, Assumptions for Performing a t-test, Types of t-tests, One sample t-test, Independent two-sample t-test and Paired sample t-test.
For more topics Stay tuned with Learnbay
Discrete and continuous probability distributions ppt @ bec domsBabasab Patil
The document discusses various probability distributions including discrete and continuous distributions. It covers the binomial, hypergeometric, Poisson, and normal distributions. It provides the characteristics and formulas for each distribution and examples of how to calculate probabilities using the distributions.
A one-sample z-test is used to compare a sample proportion to a population proportion. The document provides an example where a survey claims 90% of doctors recommend aspirin, and a sample of 100 doctors found 82% recommend aspirin. The z-test is calculated to determine if this difference is statistically significant. The null hypothesis is the sample and population proportions are the same. If the calculated z-statistic falls outside the critical values of -1.96 and 1.96, the null will be rejected, meaning the proportions are significantly different.
Correlation by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari
The regression coefficients are 0.8 and 0.2.
The coefficient of correlation r is the geometric mean of the regression coefficients, which is:
√(0.8 × 0.2) = 0.4
Therefore, the value of the coefficient of correlation is 0.4.
This document provides an introduction to basic statistics and regression analysis. It defines regression as relating to or predicting one variable based on another. Regression analysis is useful for economics and business. The document outlines the objectives of understanding simple linear regression, regression coefficients, and merits and demerits of regression analysis. It describes types of regression including simple and multiple regression. Key concepts explained in more detail include regression lines, regression equations, regression coefficients, and the difference between correlation and regression. Examples are provided to demonstrate calculating regression equations using different methods.
The document discusses simple linear regression analysis. It provides definitions and formulas for simple linear regression, including that the regression equation is y = a + bx. An example is shown of using the stepwise method to determine if there is a significant relationship between number of absences (x) and grades (y) for students. The analysis finds a significant negative relationship, meaning more absences correlated with lower grades. Formulas are provided for calculating the slope, intercept, and testing significance of the regression model.
Regression Analysis is simplified in this presentation. Starting with simple linear to multiple regression analysis, it covers all the statistics and interpretation of various diagnostic plots. Besides, how to verify regression assumptions and some advance concepts of choosing best models makes the slides more useful SAS program codes of two examples are also included.
Regression analysis measures the average relationship between two or more variables using their original data units. There are two main types: simple regression involving two variables, and multiple regression involving more than two variables. Regression can be linear, following a straight line, or non-linear/curvilinear. A simple linear regression model relates a dependent variable Y to an independent variable X plus an error term. Estimating the model involves calculating the slope/regression coefficient and intercept. Multiple regression relates a dependent variable to two or more independent variables using a multiple correlation coefficient.
Here are the key steps and results:
1. Load the data and run a multiple linear regression with x1 as the target and x2, x3 as predictors.
R-squared is 0.89
2. Add x4, x5 as additional predictors.
R-squared increases to 0.94
3. Add x6, x7 as additional predictors.
R-squared further increases to 0.98
So as more predictors are added, the R-squared value increases, indicating more of the variation in x1 is explained by the model. However, adding too many predictors can lead to overfitting.
The document discusses regression and correlation analysis. It defines regression analysis as estimating the values of one variable from knowledge of another variable. Correlation analysis measures the strength of association between variables. Regression analysis can be linear, exponential, logarithmic or power. Linear regression finds the best-fit straight line to describe the relationship between two variables. The correlation coefficient measures the extent of correlation between -1 and 1. Values above the critical t-value indicate a significant correlation. Examples are provided to demonstrate calculating the linear regression equation and correlation coefficient.
Through this ppt you could learn what is Wilcoxon Signed Ranked Test. This will teach you the condition and criteria where it can be run and the way to use the test.
The document discusses a one-way ANOVA test, which compares the means of two or more independent groups on a continuous dependent variable. It outlines the assumptions of the test, how to set it up in SPSS, and how to interpret the output. Key outputs include an ANOVA table showing if group means are statistically significantly different, and a post-hoc test for determining the nature of differences between specific groups.
Mpc 006 - 02-03 partial and multiple correlationVasant Kothari
3.2 Partial Correlation (rp)
3.2.1 Formula and Example
3.2.2 Alternative Use of Partial Correlation
3.3 Linear Regression
3.4 Part Correlation (Semipartial correlation) rsp
3.4.1 Semipartial Correlation: Alternative Understanding
3.5 Multiple Correlation Coefficient (R)
The Statistical Inference is the process of drawing conclusions about on underlying population based on a sample or subset of the data.
In most cases, it is not practical to obtain all the measurements in a given population.
The statistical inference is deals with decision problems. There are two types of decision problems as mentioned below:
(i) Problems of estimation and
(ii) Test of hypotheses
In the problem of estimation, we must determine the value of parameter(s), while in test of hypothesis we must decide whether to accept or reject a specific value(s) of a parameter(s).
This document discusses hypothesis testing and the t-test. It covers:
1) The basics of hypothesis testing including null and alternative hypotheses, types of hypotheses, and types of errors.
2) The t-test, which is used for small samples from a normally distributed population. It relies on the t-distribution and the degree of freedom.
3) Applications of the t-test including testing the significance of a single mean, difference between two means, and paired t-tests.
4) When sample sizes are large, the normal distribution can be used instead in Z-tests for similar applications.
The document discusses hypothesis testing and provides examples to illustrate the process. It explains how to state the research question and hypotheses, set the decision rule, calculate test statistics, decide if results are significant, and interpret the findings. An example tests if narcissistic individuals look in the mirror more often than others and finds they do based on a test statistic exceeding the critical value. A second example finds no significant difference in recovery time for patients with or without social support after surgery.
Correlation & Regression Analysis using SPSSParag Shah
Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
- Regression analysis is a statistical technique for modeling relationships between variables, where one variable is dependent on the others. It allows predicting the average value of the dependent variable based on the independent variables.
- The key assumptions of regression models are that the error terms are normally distributed with zero mean and constant variance, and are independent of each other.
- Linear regression specifies that the dependent variable is a linear combination of the parameters, though the independent variables need not be linearly related. In simple linear regression with one independent variable, the least squares estimates of the intercept and slope are calculated to minimize the sum of squared errors.
Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six –Sigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
This presentation educates you about T-Test, Key takeways, Assumptions for Performing a t-test, Types of t-tests, One sample t-test, Independent two-sample t-test and Paired sample t-test.
For more topics Stay tuned with Learnbay
Discrete and continuous probability distributions ppt @ bec domsBabasab Patil
The document discusses various probability distributions including discrete and continuous distributions. It covers the binomial, hypergeometric, Poisson, and normal distributions. It provides the characteristics and formulas for each distribution and examples of how to calculate probabilities using the distributions.
A one-sample z-test is used to compare a sample proportion to a population proportion. The document provides an example where a survey claims 90% of doctors recommend aspirin, and a sample of 100 doctors found 82% recommend aspirin. The z-test is calculated to determine if this difference is statistically significant. The null hypothesis is the sample and population proportions are the same. If the calculated z-statistic falls outside the critical values of -1.96 and 1.96, the null will be rejected, meaning the proportions are significantly different.
Correlation by Neeraj Bhandari ( Surkhet.Nepal )Neeraj Bhandari
The regression coefficients are 0.8 and 0.2.
The coefficient of correlation r is the geometric mean of the regression coefficients, which is:
√(0.8 × 0.2) = 0.4
Therefore, the value of the coefficient of correlation is 0.4.
This document provides an introduction to basic statistics and regression analysis. It defines regression as relating to or predicting one variable based on another. Regression analysis is useful for economics and business. The document outlines the objectives of understanding simple linear regression, regression coefficients, and merits and demerits of regression analysis. It describes types of regression including simple and multiple regression. Key concepts explained in more detail include regression lines, regression equations, regression coefficients, and the difference between correlation and regression. Examples are provided to demonstrate calculating regression equations using different methods.
The document discusses regression analysis, including definitions, uses, calculating regression equations from data, graphing regression lines, the standard error of estimate, and limitations. Regression analysis is a statistical technique used to understand the relationship between variables and allow for predictions. The document provides examples of calculating regression equations from various data sets and determining the standard error of estimate.
This presentation covered the following topics:
1. Definition of Correlation and Regression
2. Meaning of Correlation and Regression
3. Types of Correlation and Regression
4. Karl Pearson's methods of correlation
5. Bivariate Grouped data method
6. Spearman's Rank correlation Method
7. Scattered diagram method
8. Interpretation of correlation coefficient
9. Lines of Regression
10. regression Equations
11. Difference between correlation and regression
12. Related examples
Biostats coorelation vs rREGRESSION.DIFFERENCE BETWEEN CORRELATION AND REGRES...Payaamvohra1
CORRELATION
REGRESSION
BIOSTATISTICS
SEMESTER 8
M PHARMACY
CORRELATION VS REGRESSION
REGRESSION ANALYSIS
LINEAR AND MULTIPLE REGREISSIO
CORRELATION COEFFICIENT
1. Regression analysis is a statistical technique used to model relationships between variables and make predictions. It can be used to describe relationships, estimate coefficients, make predictions, and control systems.
2. Linear regression models describe straight-line relationships between variables, while non-linear models describe curved relationships. The goodness of fit of a model can be evaluated using the coefficient of determination.
3. The least squares method is used to fit regression lines by minimizing the sum of the squared vertical distances between observed and estimated y-values for a regression of y on x, or minimizing the sum of squared horizontal distances for a regression of x on y.
This document provides an introduction to regression and correlation analysis. It discusses simple and multiple linear regression models, how to interpret regression coefficients, and how to check the assumptions and adequacy of regression models. Key aspects covered include computing the regression line using the least squares method, interpreting the slope and intercept, checking the normality of residuals, and examining residual plots to validate the model. The goal of regression analysis is to model the relationship between a dependent variable and one or more independent variables.
CORRELATION-AND-REGRESSION.pdf for human resourceSharon517605
This document discusses correlation and regression analysis. It defines correlation as measuring the relationship between two quantitative variables. There are two main correlation coefficients - Pearson's r which measures the strength of a linear relationship between two variables, and Spearman's Rho which measures the monotonic relationship between two ranked variables. The document also discusses scatter plots/diagrams which can help visualize the relationship between two variables, and defines different types of correlations such as positive, negative, simple, partial and multiple correlations. It provides examples of how to calculate Pearson's r correlation coefficient and how to interpret the resulting value.
This document provides an overview of regression analysis and two-way tables. It defines key concepts such as regression lines, correlation, residuals, and marginal and conditional distributions. Regression finds the linear relationship between two variables to make predictions. The least squares regression line minimizes the vertical distance between the data points and the line. Correlation and the coefficient of determination r2 measure how well the regression line fits the data. Two-way tables summarize the relationship between two categorical variables through marginal and conditional distributions.
Analyzing Relations between Data Set - Part INaseha Sameen
Statistics is the foundation of any data analysis. In real life experience, while analyzing data especially to interpret trend, take a decision, or to find the influencer. This is the first set of the series, a quick reference to professionals and students to understand and implement Correlation, Covariance and Regression.
The document discusses correlation and regression, explaining that correlation describes the strength of a linear relationship between two variables, while regression tells us how to draw the straight line described by the correlation. It provides examples of using correlation coefficients to determine the strength and direction of relationships between independent and dependent variables, and discusses calculating correlation coefficients and using regression analysis to predict variable relationships and outcomes.
Linear regression was used to analyze the relationship between daily food intake (independent variable) and weight gain (dependent variable) in a sample of 20 children. The regression equation obtained was: Weight gained = 0.16 + 0.643(food weight). This indicates that for each additional 1kg of daily food intake, a child's weight increases by 0.643kg on average. The coefficient of determination (R2) was 0.81, meaning 81% of the variation in children's weight gain was explained by differences in daily food intake.
Unit-III Correlation and Regression.pptxAnusuya123
Unit-III describes different types of relationships between variables through correlation and regression analysis. It discusses:
1) Correlation measures the strength and direction of a linear relationship between two variables on a scatter plot. Positive correlation means variables increase together, while negative correlation means one increases as the other decreases.
2) Regression analysis uses independent variables to predict outcomes of a dependent variable. A regression line minimizes the squared errors between predicted and actual values.
3) The correlation coefficient r and coefficient of determination r-squared quantify the strength and direction of linear relationships, with values between -1 and 1. Extreme scores on one measurement tend to regress toward the mean on subsequent measurements.
This document discusses correlation and regression. Correlation describes the strength and direction of a linear relationship between two variables, while regression allows predicting a dependent variable from an independent variable. It provides examples of calculating the correlation coefficient r to determine the strength and direction of relationships between variables like education and self-esteem or family income and number of children. The regression equation describes the linear regression line and can be used to predict values of the dependent variable from known values of the independent variable.
The document presents a regression analysis on the relationship between driving experience (the independent variable X) and the number of road accidents (the dependent variable Y). It finds the regression line to be Y = 76.66 - 1.5476X, indicating a negative relationship between accidents and experience. Using this line, it estimates the number of accidents would be 61.184 for 10 years experience and 30.232 for 30 years experience. It also calculates the coefficient of determination R2 = 0.5894, meaning driving experience explains around 59% of the variance in road accidents.
This document discusses correlation and regression analysis. It defines correlation as assessing the relationship between two variables, while regression determines how well one variable can predict another. Correlation does not imply causation. Pearson's r standardizes the covariance between variables and ranges from -1 to 1, indicating the strength and direction of their linear relationship. Regression finds the best-fitting linear relationship through the least squares method to minimize residuals and predict one variable from another. It provides the slope and intercept of the regression line. The coefficient of determination, r-squared, indicates how well the regression model fits the data.
To get a copy of the slides for free Email me at: japhethmuthama@gmail.com
You can also support my PhD studies by donating a 1 dollar to my PayPal.
PayPal ID is japhethmuthama@gmail.com
To get a copy of the slides for free Email me at: japhethmuthama@gmail.com
You can also support my PhD studies by donating a 1 dollar to my PayPal.
PayPal ID is japhethmuthama@gmail.com
This document summarizes key concepts from Chapter 5 of Jamri AB on correlation and simple linear regression. It introduces correlation as a measure of the strength of the linear relationship between two variables. It discusses scatter diagrams, the coefficient of correlation (r), and Pearson's product-moment correlation coefficient and Spearman's rank correlation coefficient as methods to calculate r. It also covers the coefficient of determination (r^2), linear regression analysis to predict relationships, and calculating the regression equation coefficients a and b. Examples are provided to demonstrate calculating r and the regression equation from sets of data.
The document discusses mergers and acquisitions. It defines mergers as a transaction where two firms integrate operations to create a stronger competitive advantage. It describes different types of mergers such as horizontal, vertical, conglomerate, market extension, and product extension mergers. Acquisitions are defined as one company purchasing another. The key difference between mergers and acquisitions is that mergers form a new company while acquisitions do not. Synergy effects are cited as a driving force behind M&A deals. The regulatory framework around M&As in India is also summarized.
The document discusses the Foreign Exchange Management Act (FEMA) and its regulations regarding the remittance of assets. FEMA was introduced in 2000 to consolidate and amend laws relating to foreign exchange. It aims to facilitate external trade and payments. The Foreign Exchange Management (Remittance of Assets) Regulations, 2016 place various prohibitions and permissions regarding the remittance of assets held in India. These include prohibiting remittance without permission, and permitting remittance in cases such as inheritance, winding up of offices, and payment of taxes in accordance with Indian law.
The document outlines the steps to formulate a hypothesis for research. It defines what a hypothesis is, discusses the types of hypotheses (null and alternative), and lists advantages of developing a hypothesis. The key steps provided are: define the research problem, analyze the problem in-depth, define research objectives, and articulate the hypothesis. Hypotheses can be developed through various means like literature review, observations, and prior studies. The document also provides an example of formulating hypotheses for a study on customer preferences and usage of cashless payments.
The document discusses the evolution of e-banking and various technologies used in the banking sector. It describes traditional banking services and the emergence of electronic delivery channels like ATMs, debit/credit cards, internet banking, mobile banking, RTGS and NEFT systems. While e-banking provides benefits like convenience, speed and lower costs, security issues remain a challenge. Both banks and customers must take steps to reduce security threats in order to increase popularity of e-banking.
This document discusses various cooperative organizations that operate in rural areas in India. It defines a cooperative organization as one that promotes the economic interests of its members according to cooperative principles. It describes several cooperative organizations that provide various services to rural communities like agricultural credit, marketing and storage facilities, and socioeconomic development. Some organizations discussed include the Shri Mahila Griha Udyog Lijjat Papad cooperative, Jan Vikas cooperative society, Lokmanya cooperative credit society, Tribal Cooperative Marketing Development Federation of India, National Agricultural Cooperative Marketing Federation of India, and National Tree Growers Cooperative Federation.
This document discusses brand positioning and the use of perceptual positioning maps, specifically Centrality-Distinctiveness (C-D) maps, as strategic tools. It explains that C-D maps allow companies to measure consumer perceptions of a brand's centrality and distinctiveness compared to competitors on a 2x2 matrix. The size of bubbles representing each brand indicates its relative market performance. C-D maps can help companies identify positioning opportunities, threats from competitors, and guide resource allocation and brand strategy decisions. While useful, C-D maps alone may not capture all factors like product features that influence pricing and sales.
SEBI was established in 1988 as a non-statutory body and was given statutory powers through the SEBI Act in 1992. SEBI regulates the securities market in India by promoting its orderly and healthy development. It aims to protect investors, maintain fair practices, and ensure transparency through regulating stock exchanges, intermediaries, and other market participants. SEBI performs protective, developmental and regulatory functions like prohibiting unfair trade practices, promoting training and activities, and registering and regulating various intermediaries and institutions.
Economic implications of the Indian Constitutionsimran sakshi
The Indian Constitution lays out several economic implications for businesses. It establishes the right to equality, freedom, and prevents exploitation in the workplace. The Directive Principles of State Policy guide government policies to protect workers and prevent wealth concentration. The Constitution also enables free trade between states while allowing reasonable restrictions in the public interest. Overall, the document establishes a framework for economic justice, equal opportunity, and regulating business in accordance with fundamental rights.
Indian Economy - old wine in new bottlesimran sakshi
The document discusses whether the Indian economy under the Modi government is "old wine in new bottle" or "new wine in old bottle". It provides an overview of the Indian economy and key reforms by the Modi government. While some positive changes have occurred like increased FDI, manufacturing targets, and subsidy reforms through Aadhaar, some challenges remain around job creation, wealth distribution, and addressing bad loans. Overall the reforms have been steady but incremental, with some doubting the pace and impact of changes.
Fastrack was launched in 1998 as a sub-brand of Titan for watches. It was relaunched in 2005 as an independent brand with new products, identity, advertising, and logo. Fastrack is now Titan's most profitable brand, contributing 30-40% of Titan's profits. Fastrack targets youth, especially students who make up 30% of sales. It has a growing product line beyond watches and a strategy of trendy and affordable designs. Fastrack aims to increase its market share and expand globally through new stores and product lines.
_Lufthansa Airlines MIA Terminal (1).pdfrc76967005
Lufthansa Airlines MIA Terminal is the highest level of luxury and convenience at Miami International Airport (MIA). Through the use of contemporary facilities, roomy seating, and quick check-in desks, travelers may have a stress-free journey. Smooth navigation is ensured by the terminal's well-organized layout and obvious signage, and travelers may unwind in the premium lounges while they wait for their flight. Regardless of your purpose for travel, Lufthansa's MIA terminal
Do People Really Know Their Fertility Intentions? Correspondence between Sel...Xiao Xu
Fertility intention data from surveys often serve as a crucial component in modeling fertility behaviors. Yet, the persistent gap between stated intentions and actual fertility decisions, coupled with the prevalence of uncertain responses, has cast doubt on the overall utility of intentions and sparked controversies about their nature. In this study, we use survey data from a representative sample of Dutch women. With the help of open-ended questions (OEQs) on fertility and Natural Language Processing (NLP) methods, we are able to conduct an in-depth analysis of fertility narratives. Specifically, we annotate the (expert) perceived fertility intentions of respondents and compare them to their self-reported intentions from the survey. Through this analysis, we aim to reveal the disparities between self-reported intentions and the narratives. Furthermore, by applying neural topic modeling methods, we could uncover which topics and characteristics are more prevalent among respondents who exhibit a significant discrepancy between their stated intentions and their probable future behavior, as reflected in their narratives.
Essential Skills for Family Assessment - Marital and Family Therapy and Couns...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
3. INTRODUCTION
o The dictionary meaning of the term “Regression” is the act of
returning or going back.
o The term regression was first used by sir “Francis Galton” in
1877 while studying the relationship between the height of
fathers and sons.
o This term introduced by him in the paper “Regression towards
mediocrity in hereditary stature”.
4. o “Regression is the measure of the average relationship
between two or more variables in terms of the original units of
the data.”
- Blair
“The term regression analysis refers to the methods by which
estimates are made of the variables from a knowledge of the
values of one or more other variables and to the measurement
of the errors involved in the estimation.”
- Morris Hamburg
Definition of Regression
5. Difference between Correlation and
Regression
S. NO.
Correlation Regression
1. Correlation coefficient is a
measure of degree of co-
variability or association
between X and Y.
The objective of regression
analyses is to the study of
nature of relationship
between the variables so
that we may be able to
predict the values of one on
the basis of another.
6. S. NO Correlation Regression
2. It is merely a tool of ascertaining
the degree of relationship
between two variable and,
therefore, we cannot say that
one variable is the cause and
the other is effect. The variables
may be affected by some
unknown common factor.
In regression analysis one variable is
taken as dependent while the other as
independent-thus making it possible to
study the cause and effect relationship.
3. Correlation coefficient is
independent of change of scale
and origin.
Regression coefficient is independent
of change of origin but not of scale.
7. S.
NO
Correlation Regression
4. In this 𝑟𝑥𝑦 is a measure of direction
and degree of linear relationship
between two variable X and Y. 𝑟𝑦𝑥
and 𝑟𝑥𝑦 are symmetric, it is
immaterial which of X and Y is
dependent variable and which is
independent variable.
In regression analyses the regression
coefficients 𝑏 𝑥𝑦 and 𝑏 𝑦𝑥 are not
symmetric, and hence it definitely
makes a difference as to which
variable is dependent and which is
independent.
8. Types of Regression
Linear Regression Logical Regression
Polynomial
Regression
Stepwise
Regression
Ridge Regression Lasso Regression
12. Y= b0 + b1x + Ԑ
E(Y) = b0 + b1x
Ŷ = b0 + b1x
SIMPLE LINEAR REGRESSION MODEL
SIMPLE LINEAR REGRESSION EQUATION
ESTIMATED SIMPLE LINEAR REGRESSION EQUATION
13. REGRESSION
GRAPHICALLY FREE HAND CURVE
LEAST SQUARES
ALGEBRAICALLY
LEAST SQUARES
DEVIATION
METHOD FROM
ARITHMETIC
MEAN
DEVIATION
METHOD FROM
ASSUMED MEAN
14. Least Square Method
A procedure for using sample data to find the estimated regression equation.
It uses the sample data method to provide the values of b0 and b1 that minimize
the sum of the squares of the deviations between the observed values of the
dependent variable Y and the estimated values of the dependent variable Ŷ.
The criterion for the least squares method is given as: min ∑(Yi – Ŷi)2
The error on either side of the regression line has to be minimized.
34. R-square or Coefficient of determination
R squared or coefficient of determination indicates the proportionate amount of
variation in the responsible variable y explained by the independent variables x in
the linear regression model.
It provides a good measure of how well the estimated regression equation fits the
data.
The larger the R-squared is, the more variability is explained by the linear regression
model.
The closer r2 is +1, the better the line fits the data.
r2 will always be a positive number.
R2 = 1 indicates that the regression line perfectly fits the data.
35. X Y
3 40
10 35
11 30
15 32
22 19
22 26
23 24
28 22
28 18
35 6 Equation for Line of Best Fit: y = -.94x + 43.7
Example: To calculate R-square
36. X Y
Predicted Y
Value
Error
(predicted
value-y)
Error
Squared
Distance
between Y values
and their mean
Mean
distances
squared
3 40 40.88 .88 .77 14.8 219.04
10 35 34.30 -.70 .49 9.8 96.04
11 30 33.36 3.36 11.29 4.8 23.04
15 32 29.60 -2.40 5.76 6.8 46.24
22 19 23.02 4.02 16.16 -6.2 38.44
22 26 23.02 -2.98 8.88 .8 .64
23 24 22.08 -1.92 3.69 -1.2 1.44
28 22 17.38 -4.62 21.34 -3.2 10.24
28 18 17.38 -.62 .38 -7.2 51.84
35 6 10.80 4.8 23.04 -19.2 368.65
Mean: 25.2 Sum: 91.81 Sum: 855.60
Equation for Line of Best Fit: y = -.94x + 43.7
37. 1-
Sum of squared distances between the
actual and predicted Y values
Sum of squared distances between the
actual Y values and their mean
1-
91.81
855.60
= 1- 0.11
= 0.89
R2 =
38. Or
Correlation = -.94
To calculate R-square, we
square the correlation.
Thus, r2= -0.942= 0.89
Equation for Line of Best Fit: y = -.94x + 43.7
39. Adjusted R-square is a modification of R-square that adjusts
for the number of terms in a model.
R-square always increases when a new term is added to a
model, but adjusted R-square increases only if the new term
improves the model more than would be expected by chance.
This makes Adjusted R-square more useful for comparing
models with a different number of predictors.
R-squared increases if we increase the number of
variables in the regression model.
R squared, a property of the fitted model, is a structure with two fields:
•Ordinary — Ordinary (unadjusted) R-squared
•Adjusted — R-squared adjusted for the number of coefficients
40. Uses of Regression Analysis
Helps in establishing a functional relationship between two or more
variables
As most of the problems of economic analysis is based on cause and
effect relationships, regression analysis is a highly valuable tool in
economics and business research
It predicts the values of dependent variables from the values of
independent variables
We can calculate the coefficient of correlation and coefficient of
determination with the help of regression coefficients
42. o In making estimates from a regression equation, it
is important to remember that the assumption is
being made that relationship has not changed since
the regression equation was computed.
Another point worth remembering is that
relationship shown by the scatter diagram, may not
be the same if the equation is extended beyond the
values used in computing the equation.
Limitations of Regression
43. o for example
there may be a close linear relationship between
the yield of a crop and the amount of fertilizer
applied, with the yield increasing as the amount
of fertilizer is increased. It would not be logical,
however, to extend this equation beyond the
limits of experiment for it is quite likely that if the
amount of fertilizer were increase indefinitely, the
yield would eventually decline as too much
fertilizer was applied.
雅虎竞拍
煤炉代买
paypay商城
乐天二手
日本亚马逊
乐天新品
ZOZOTOWN
