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# Regression & Time series analysis

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12.48 In the following regression, X = weekly pay, Y = income tax withheld, and n = 35.

R(squared) 0.202
Standard Error 6.816
n 35

ANOVA Table
Source SS df MS f P-value
Regression 387.6959 1 387.6959 8.35 .0068
Residual 1,533.0664 33 46.4564
Total 1,920.7573 34

Regression Output Confidence Interval
Variables Coeficient Std. error t(df=33) pvalue 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

(a) Develop and State the fitted regression equation.

(b) Use the above table, and state the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at.

(c) What is your conclusion about the slope? Use the appropriate value from the above table, and provide appropriate explanation!

(d) Interpret the 95 percent confidence interval limits for the slope. Use the appropriate limits from the above table, and provide appropriate explanation!

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.

Variable Coeficiant 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

R(squared) = 0.811 R(squared ADJ)=0.809 s = 3,318

Dependent variable: Year (Year in which the salary was observed)
Predictors:
Year Hire (year when the individual was hired)
Race (1 if individual is black, 0 otherwise)
Rank (1 if individual is assistant professor, 0 otherwise)

(a) What percent of the variation in Salary can be explained by the predictor variables as a group? Does the regression as a whole indicates a very strong fit? Why or Why not? Explain.

(b) In examining the individual regression coefficients, can you decide/indicate which of the predicator variables are significantly different from zero? Why or Why not? Explain.

(c) Using the appropriate figures from the above table of results, can you explain as to whether the ethnicity of a professor matters? Why or Why not?

(d) Using the appropriate figures from the above table of results, can you explain as to whether on average assistant professors earn less that full professors? And if so by how much?

Chapter Exercises 14.16
The following table represents U.S. Manufactured General Aviation Shipments. 1966-2003.

US Manufactured General Aviation Shipments
Yrs Planes Yrs Planes Yrs Planes Yrs 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 9,744 1982 4,266 1992 856 2002 2,169
1973 13,646 1983 2,691 1993 870 2003 2,190
1974 14,166 1984 2,431 1994 881
1975 14,056 1985 2,029 1995 1,028

(a) Plot the above data. (Using Technology: i.e. Excel or MegaStat). Copy your graph to this Word document. Describe the pattern and discuss possible causes

(b) Plot a similar graph of the subset of data starting from 1992 and going through 2003. Copy your graph to this Word document. Describe the pattern.

(c) Fit an exponential trend to the plot you have exhibited in part (b), above. State the exponential fit equation. Would the exponential trend model be helpful in making a prediction for 2004? Make a forecast for 2004, using the fitted trend model, and another forecast for 2004, by just using a judgment forecast, just by eyeballing the most recent data.

(d) In part (b), we choose a subset (1992-2003). Why is it best to ignore earlier years in this data set. Explain!