C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 1 Correlation and Simple Linear Regression Analysis C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 2 Learning Objectives Upon completion of this chapter, you will be able to: Ø Use the simple linear regression equation Ø Compute the coefficient of correlation and understand its interpretation. Ø Understand the concept of measures of variation, coefficient of determination, and standard error of the estimate Ø Understand and use residual analysis for testing the assumptions of regression Ø Measure autocorrelation by using the Durbin–Watson statistic Ø Understand statistical inference about slope, correlation coefficient of the regression model, and testing the overall model C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 3 Measures of Association Ø Measures of association are statistics for measuring the strength of relationship between two variables. Ø Correlation measures the degree of association between two variables. Ø Karl Pearson’s coefficient of correlation is a quantitative measure of the degree of relationship between two variables. Suppose these variables are x and y, then Karl Pearson’s coefficient of correlation is defined as Ø The coefficient of correlation lies in between +1 and –1. C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 4 Figure 15.1: Interpretation of correlation coefficient C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 5 Table 15.2 shows the sales revenue and advertisement expenses of a company for the past 10 months. Find the coefficient of correlation between sales and advertisement. Example 15.1 C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 6 Table 15.3 : Calculation of correlation coefficient between sales and advertisement C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 7 Figure 15.9: Five examples of correlation coefficient C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 8 Using MS Excel, Minitab and SPSS for Computing Correlation Coefficient Ø Ch 15 Solved Examples\Excel\Ex 15.1.xls Ø Ch 15 Solved Examples\Minitab\Ex 15.1.MPJ Ø Ch 15 Solved Examples\SPSS\Ex 15.1.sav Ø Ch 15 Solved Examples\SPSS\Output Ex 15.1.spv C o p yr ig h t© D o rl in g K in d er sl ey I n d ia P vt . Lt d Correlation and Simple Linear Regression Analysis 9 Introduction to .