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    Statistics: Regression and ANOVA Analysis Questions

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    In the following regression, x=weekly pay, Y= income tax with held, and n=35 Mc Donald's employees. A. writes the fitted regression equation.

    B. state the degrees of freedom for a two-tailed test for zero slope, and use to find the critical value at a =.05.
    C. what is your conclusion about the slope?
    D. Interpret the 95 percent confidence limits for the slope
    E. Verify the 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
    Residual 387.6959 1 387.6959 8.35 .0068

    Residual 1533.0614 33 46.4564

    Total 1,920.7573 34

    Regression Output confidence interval
    Variables coefficients std. t(df p-value 95% 95%
    Error =33) lower 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

    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. Find the critical value at a=.05.
    c. c. what is your conclusion about the slope?
    d. Interpret the 95 percent confidence limits for the slope.
    e. Verify the F=t² for the slope.
    f. In your own words, describe the fit of this regression.

    R= 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 t (df p-value 95% 95%
    Error =62) lower 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

    3.
    A researcher used stepwise regression to create regression models to predict birthrate( births per 1,000) using five predictors: lifeExp (life expectancy in years), infMort (infant mortality rate), Density (population density per square Kilometers), GDP Cap (gross Domestic Product per capita), and Literate (Literacy percent). Interpret these results.

    Regression Analysis-stepwise selection ( best model of each size)
    153 observations
    Birthrate is the dependent variable
    P-values for the coefficients

    Nvar lifeExp InfMort Density GDPCap Literate s Adj R² R²
    1 .0000 6.318 .722 .724
    2 .0000 .0000 5.334 .802 .805
    3 .0000 .0242 .0000 5.261 .807 .811
    4 .5764 .0000 .0311 .0000 5.273 .806 .812
    5 .5937 .0000 .6289 .0440 .0000 5.287 .805 .812

    4. An expert witness in 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 (1if individual is an assistant professor, 0 otherwise). Interpret these results.

    Variable Coefficient t p
    Intercept -3,816,521 -29.4 .000
    Year 1,948 29.8 .000
    YearHire -826 -5.5 .000
    Race -2,093 -4.3 .000
    Rank -6,438 -22.3 .000

    Rank -6,438 -22.3 .000

    R²= 0.811 R² adj =0.809 s=3,318

    5.
    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 1992-2003 only. would a fitted trend be helpful in making a prediction for 2004?
    e. Fit a trend model of your choice to the 1992-2003 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? Airplanes

    U.S Manufactured General Aviation Shipments, 1966-2003
    Year
    1966 15,587
    1967 13,484
    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

    Source : U.S Manufactured General Aviation Shipments, Statistical Databook 2003, General Aviation Manufacturers Association, Used with permission.

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    The solution provides a regression analysis of employees and income tax.

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