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1. (a) How does correlation analysis differ from regression…

1. (a) How...

1. (a) How does correlation analysis differ from regression analysis? (b) What does a correlation coefficient reveal? (c) State the quick rule for a significant correlation and explain its limitations. (d) What sums are needed to calculate a correlation coefficient? (e) What are the two ways of testing a correlation coefficient for significance? 2. In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees. (a) Write the fitted regression equation. (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. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression. R2 0.202 Std. Error 6.816 n 35 ANOVA table Source SS df MS F p-value Regression SS:(NNN) NNN-NNNNdf: 1 MS:(NNN) NNN-NNNNF: 8.35 p-value: .0068 Residual SS: 1,533.0614 df: 33 MS: 46.4564 Total SS: 1,920.7573 df: 34 Regression output Confidence interval variables coefficients std. error t (df = 33) p-value 95% lower 95% upper Intercept coefficients: 30.7963 std. error: 6.4078 t (df = 33): 4.806 .0000 95% lower: 17.7595 95% upper: 43.8331 Slope coefficients: 0.0343 std. error: 0.0119 t (df = 33): 2.889 p-value: 0068 95% lower: 0.0101 95% upper: 0.0584 3. In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fitted regression equation. (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. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression. R2 0.519 Std. Error 6.977 n 64 ANOVA table Source SS df MS F p-value 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 Total SS: 6,278.4320 df: 63 Regression output confidence interval variables coefficients std. error t (df = 62) p-value 95% lower 95% upper Intercept coefficients: 6.5763 std. error: 1.9254 t (df = 62): 3.416 p-value: .0011 95% lower: 2.7275 95% upper: 10.4252 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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7/18/2010

Tutor: StatisticsExpert, Professor replied 10 years ago

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Customer reply replied 10 years ago

I'll try the paste from word button. Please let me know if this helps.

If you can't help tonight, please pass this along to someone else. Thanks!

1.
(a) How does correlation analysis differ from regression analysis?

(b) What does a correlation coefficient reveal?

(c) State the quick rule for a significant correlation and explain its limitations.

(d) What sums are needed to calculate a correlation coefficient?

(e) What are the two ways of testing a correlation coefficient for significance?

2.
In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.

R2 0.202

Std. Error 6.816

n 35

ANOVA table

Source SS df MS F p-value

Regression SS:(NNN) NNN-NNNNdf: 1 MS:(NNN) NNN-NNNNF: 8.35 p-value: .0068

Residual SS: 1,533.0614 df: 33 MS: 46.4564

Total SS: 1,920.7573 df: 34

Regression output Confidence interval

variables coefficients std. error t (df = 33) p-value 95% lower 95% upper

Intercept coefficients: 30.7963 std. error: 6.4078 t (df = 33): 4.806 .0000 95% lower: 17.7595 95% upper: 43.8331

Slope coefficients: 0.0343 std. error: 0.0119 t (df = 33): 2.889 p-value: 0068 95% lower: 0.0101 95% upper: 0.0584

3.
In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.

R2 0.519

Std. Error 6.977

n 64

ANOVA table

Source SS df MS F p-value

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

Total SS: 6,278.4320 df: 63

Regression output confidence interval

variables coefficients std. error t (df = 62) p-value 95% lower 95% upper

Intercept coefficients: 6.5763 std. error: 1.9254 t (df = 62): 3.416 p-value: .0011 95% lower: 2.7275 95% upper: 10.4252

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

Customer reply replied 10 years ago

Did that help? Please let me know. Thank you.

Tutor: StatisticsExpert, Professor replied 10 years ago

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Customer reply replied 10 years ago

Thank you. I have another set of questions posted if you have time.

Customer reply replied 10 years ago

I have three sets of questions posted if you have time; one is all true or false, the other two are multiple choice.

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