Res 342 Wk 5 Chapter Exercises

Chapter Exercises

Christa Christian

University of Phoenix

Kent Moser

RES 342/ Research and Evaluation II

April 7, 2011

Chapter Exercises

Ch. 12 Review #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?

c) The quick rule for significant correlation is used when the t test is unavailable. This quick rule is derived from formula 12.5 by inserting 2 in place of tα. It is based on the fact that two-tail t-values for α = .05 usually are not far from 2. This quick rule is exact for ν = 60 and works reasonably well as long as n is not too small. While a larger sample does give a better estimate of the true value of ρ, a larger sample does not mean that the correlation is stronger nor does its increased significance imply increased importance.

12.48 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.

a) The fitted regression equation is the y intercept plus the slope of the regression line. We see that Income Tax Withheld = 30.7963 + .343(Weekly Pay).

b) There is a surprising amount of disagreement on the degrees of freedom for the significance of a slope, either (N, N-1 or N-2). This output shows us N-2, so there are 33 degrees of freedom. The critical value of the t for alpha of .05 and 33 degrees of freedom can be found using the excel function...