# 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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