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1. <br />(a) How...

1. <br />(a) How does correlation analysis differ from regression analysis? <br /> (b) What does a correlation coefficient reveal? <br /> (c) State the quick rule for a significant correlation and explain its limitations. <br />(d) What sums are needed to calculate a correlation coefficient? <br /> (e) What are the two ways of testing a correlation coefficient for significance? <br /><br />2. <br />In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees.<br />(a) Write the fitted regression equation. <br />(b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at a = .05. <br />(c) What is your conclusion about the slope? <br />(d) Interpret the 95 percent confidence limits for the slope. <br />(e) Verify that F = t2 for the slope. <br />(f) In your own words, describe the fit of this regression. <br /><br />R2 0.202 <br /><br />Std. Error 6.816 <br /> <br />n 35 <br /><br />ANOVA table Source SS df MS F p-value<br />Regression SS:(NNN) NNN-NNNNdf: 1 MS:(NNN) NNN-NNNNF: 8.35 p-value: .0068<br />Residual SS: 1,533.0614 df: 33 MS: 46.4564<br />Total SS: 1,920.7573 df: 34<br /><br />Regression output Confidence interval <br />variables coefficients std. error t (df = 33) p-value 95% lower 95% upper <br />Intercept coefficients: 30.7963 std. error: 6.4078 t (df = 33): 4.806 .0000 95% lower: 17.7595 95% upper: 43.8331 <br />Slope coefficients: 0.0343 std. error: 0.0119 t (df = 33): 2.889 p-value: 0068 95% lower: 0.0101 95% upper: 0.0584 <br /><br />3. <br />In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. <br />(a) Write the fitted regression equation. <br />(b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at a = .05. <br />(c) What is your conclusion about the slope? <br />(d) Interpret the 95 percent confidence limits for the slope. <br />(e) Verify that F = t2 for the slope. <br />(f) In your own words, describe the fit of this regression. <br /> <br />R2 0.519 <br /><br />Std. Error 6.977 <br /><br />n 64 <br /><br />ANOVA table <br />Source SS df MS F p-value <br />Regression SS: 3,260.0981 df: 1 MS: 3,260.0981 F: 66.97 p-value: 1.90E-11 Residual SS: 3,018.3339 df: 62 MS: 48.6828 <br />Total SS: 6,278.4320 df: 63 <br /><br />Regression output confidence interval <br />variables coefficients std. error t (df = 62) p-value 95% lower 95% upper <br />Intercept coefficients: 6.5763 std. error: 1.9254 t (df = 62): 3.416 p-value: .0011 95% lower: 2.7275 95% upper: 10.4252<br />X1 coefficients: 0.0452 std. error: 0.0055 t (df = 62): 8.183 p-value: 1.90E-11 95% lower: 0.0342 95% upper: 0.0563

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