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Regression analysis

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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

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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.

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