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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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