# Regression Analysis

For Each Equation I need (F) written out.... There are two

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.

W Y = 0.0343X + 30.7963

(b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at ± = .05.

Degrees of freedom = 34, tcrit = t34, 0.025 = 2.032244

(c) What is your conclusion about the slope?

Since t for slope is larger than the critical value, the null hypothesis is rejected.

Therefore, the population slope is different from zero.

(d) Interpret the 95 percent confidence limits for the slope.

We are 95% confident that the true population slope lies somewhere in between 0.0101 and 0.0584.

(e) Verify that F = t2 for the slope.

t2 = 2.8892 = 8.346321 = 8.35 (approx) = F

(f) In your own words, describe the fit of this regression.

12.50

In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks.

(a) Write the fitted regression equation.

Y = 0.0452X + 6.5763

(b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at ? = .05.

Degrees of freedom = 63, tcrit = t63, 0.025 = 1.998341

(c) What is your conclusion about the slope?

Since t for slope is larger than the critical value, the null hypothesis is rejected.

Therefore, the population slope is different from zero.

(d) Interpret the 95 percent confidence limits for the slope.

We are 95% confident that the true population slope lies somewhere in between 0.0342 and 0.0563.

(e) Verify that F = t2 for the slope.

t2 = 8.1832 = 66.96149 = 66.97 (approx) = F

(f) In your own words, describe the fit of this regression.

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#### Solution Summary

The solution provides step by step method for the calculation of regression model. Formula for the calculation and Interpretations of the results are also included.