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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.
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.
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.