Explore BrainMass

Explore BrainMass

    Statistics: Understanding Regression Analyses

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Question 1: 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 £ = .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 387.6959 1 387.6959 8.35 .0068
    Residual 1,533.0614 33 46.4564
    Total 1,920.7573 34
    Regression output confidence interval
    variables coefficients std. error t (df =33) p-value 95% lower 95% upper
    Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331
    Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584

    Question 2: 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 £ = .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 3,260.0981 1 3,260.0981 66.97 1.90E-11
    Residual 3,018.3339 62 48.6828
    Total 6,278.4320 63
    Regression output confidence interval
    variables coefficients std. error t (df =62) p-value 95% lower 95% upper
    Intercept 6.5763 1.9254 3.416 .0011 2.7275 10.4252
    X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563

    © BrainMass Inc. brainmass.com June 3, 2020, 10:06 pm ad1c9bdddf
    https://brainmass.com/statistics/regression-analysis/statistics-understanding-regression-analyses-215496

    Solution Preview

    Please view the attachment as well for nicer formatting.

    Question 1:
    (a) y = 0.0343x + 30.7963
    (b) Degrees of freedom (Dof) = 35 - 1 = 34, critical value of t corresponding to 34 dof at alpha = 0.05 (two-tailed) is 2.032.
    (c) Since the t- value for the slope (2.889) is greater than the critical value (2.032), the ...

    Solution Summary

    This solution is comprised of a complete, neat and step-by-step response. An attachment file is also provided which formats the ANOVA table and other variables associated with the question in a clearer manner.

    $2.19

    ADVERTISEMENT