# malhotra17.ppt - Chapter Seventeen Correlation and...

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Chapter Seventeen Correlation and Regression
17-2 Chapter Outline 1) Overview 2) Product-Moment Correlation 3) Partial Correlation 4) Nonmetric Correlation 5) Regression Analysis 6) Bivariate Regression 7) Statistics Associated with Bivariate Regression Analysis 8) Conducting Bivariate Regression Analysis i. Scatter Diagram ii. Bivariate Regression Model
17-3 Chapter Outline iii. Estimation of Parameters iv. Standardized Regression Coefficient v. Significance Testing vi. Strength and Significance of Association vii. Prediction Accuracy viii. Assumptions 9) Multiple Regression 10) Statistics Associated with Multiple Regression 11) Conducting Multiple Regression i. Partial Regression Coefficients ii. Strength of Association iii. Significance Testing iv. Examination of Residuals
17-4 Chapter Outline 12) Stepwise Regression 13) Multicollinearity 14) Relative Importance of Predictors 15) Cross Validation 16) Regression with Dummy Variables 17) Analysis of Variance and Covariance with Regression 18) Internet and Computer Applications 19) Focus on Burke 20) Summary 21) Key Terms and Concepts
17-5 Product Moment Correlation The product moment correlation , r , summarizes the strength of association between two metric (interval or ratio scaled) variables, say X and Y . It is an index used to determine whether a linear or straight-line relationship exists between X and Y . As it was originally proposed by Karl Pearson, it is also known as the Pearson correlation coefficient . It is also referred to as simple correlation , bivariate correlation , or merely the correlation coefficient .
17-6 From a sample of n observations, X and Y , the product moment correlation, r , can be calculated as: r = ( X i - X )( Y i - Y ) i =1 n ( X i - X ) 2 i =1 n ( Y i - Y ) 2 i =1 n Division of the numerator and denominator by ( n -1) gives r = ( X i - X )( Y i - Y ) n -1 i =1 n ( X i - X ) 2 n -1 i =1 n ( Y i - Y ) 2 n -1 i =1 n = COV xy S x S y Product Moment Correlation
17-7 Product Moment Correlation r varies between -1.0 and +1.0. The correlation coefficient between two variables will be the same regardless of their underlying units of measurement.
17-8 Explaining Attitude Toward the City of Residence Table 17.1 Respondent No Attitude Toward the City Duration of Residence Importance Attached to Weather 1 6 10 3 2 9 12 11 3 8 12 4 4 3 4 1 5 10 12 11 6 4 6 1 7 5 8 7 8 2 2 4 9 11 18 8 10 9 9 10 11 10 17 8 12 2 2 5
17-9 Product Moment Correlation The correlation coefficient may be calculated as follows: X = (10 + 12 + 12 + 4 + 12 + 6 + 8 + 2 + 18 + 9 + 17 + 2)/12 = 9.333 Y = (6 + 9 + 8 + 3 + 10 + 4 + 5 + 2 + 11 + 9 + 10 + 2)/12 = 6.583 ( X i - X )( Y i - Y ) i =1 n = (10 -9.33)(6-6.58) + (12-9.33)(9-6.58) + (12-9.33)(8-6.58) + (4-9.33)(3-6.58) + (12-9.33)(10-6.58) + (6-9.33)(4-6.58) + (8-9.33)(5-6.58) + (2-9.33) (2-6.58) + (18-9.33)(11-6.58) + (9-9.33)(9-6.58) + (17-9.33)(10-6.58) + (2-9.33)(2-6.58) = -0.3886 + 6.4614 + 3.7914 + 19.0814 + 9.1314 + 8.5914 + 2.1014 + 33.5714 + 38.3214 - 0.7986 + 26.2314 + 33.5714 = 179.6668
17-10 Product Moment Correlation ( X i - X ) 2 i =1 n = (10-9.33) 2 + (12-9.33) 2 + (12-9.33) 2 + (4-9.33) 2 + (12-9.33) 2 + (6-9.33) 2 + (8-9.33) 2 + (2-9.33) 2 + (18-9.33) 2 + (9-9.33) 2 + (17-9.33) 2 + (2-9.33) 2 = 0.4489 + 7.1289 + 7.1289 + 28.4089 + 7.1289+ 11.0889 + 1.7689 + 53.7289 + 75.1689 + 0.1089 + 58.8289 + 53.7289 = 304.6668 ( Y i - Y ) 2 i =1 n = (6-6.58) 2 + (9-6.58) 2 + (8-6.58) 2 + (3-6.58) 2 + (10-6.58) 2 + (4-6.58) 2 + (5-6.58) 2 + (2-6.58) 2 + (11-6.58) 2 + (9-6.58) 2 + (10-6.58) 2 + (2-6.58) 2 = 0.3364 + 5.8564 + 2.0164 + 12.8164 + 11.6964 + 6.6564 + 2.4964 + 20.9764 + 19.5364 + 5.8564 + 11.6964 + 20.9764 = 120.9168 Thus, r = 179.6668 (304.6668) (120.9168) = 0.9361
17-11 Decomposition of the Total Variation r 2 = Explained variation Total variation = SS x SS y = Total variation - Error variation Total variation = SS y - SS error SS y

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