# Regression analysis

See attached file for clarity.

Chapter 12 Review #1 (p.543)

12.48

In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonaldâ??s employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed 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 .006

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

13.32

An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Interpret these results.

Variable Coefficient t p

Intercept â?'3,816,521 â?'29.4 .000

Year 1,948 29.8 .000

YearHire â?'826 â?'5.5 .000

Race â?'2,093 â?'4.3 .000

Rank â?'6,438 â?'22.3 .000

R2 = 0.811 R2adj = 0.809 s = 3,318

14.16

(a) Plot the data on U.S. general aviation shipments. (b) Describe the pattern and discuss possible causes. (c) Would a fitted trend be helpful? Explain. (d) Make a similar graph for 1992â?"2003 only. Would a fitted trend be helpful in making a prediction for 2004? (e) Fit a trend model of your choice to the 1992â?"2003 data. (f) Make a forecast for 2004, using either the fitted trend model or a judgment forecast. Why is it best to ignore earlier years in this data set?

U.S. Manufactured General Aviation Shipments, 1966â?"2003

Year Planes Year Planes Year Planes Year Planes

1966 15,587 1976 15,451 1986 1,495 1996 1,053

1967 13,484 1977 16,904 1987 1,085 1997 1,482

1968 13,556 1978 17,811 1988 1,143 1998 2,115

1969 12,407 1979 17,048 1989 1,535 1999 2,421

1970 7,277 1980 11,877 1990 1,134 2000 2,714

1971 7,346 1981 9,457 1991 1,021 2001 2,538

1972 9,774 1982 4,266 1992 856 2002 2,169

1973 13,646 1983 2,691 1993 870 2003 2,090

1974 14,166 1984 2,431 1994 881

1975 14,056 1985 2,029 1995 1,028

Year Planes

1966 15587

1967 13484

1968 13556

1969 12407

1970 7277

1971 7346

1972 9774

1973 13646

1974 14166

1975 14056

1976 15451

1977 16904

1978 17811

1979 17048

1980 11877

1981 9457

1982 4266

1983 2691

1984 2431

1985 2029

1986 1495

1987 1085

1988 1143

1989 1535

1990 1134

1991 1021

1992 856

1993 870

1994 881

1995 1028

1996 1053

1997 1482

1998 2115

1999 2421

2000 2714

2001 2538

2002 2169

2003 2090

https://brainmass.com/statistics/regression-analysis/regression-analysis-360368

#### 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.