# Regression Analysis And Curve Fitting

What is the purpose of using regression analysis?

How might a regression analysis be used to formulate strategies?

Provide examples related to strategy formulation and implementation.

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#### Solution Preview

Regression analysis is done to predict things that might happen based upon observed data. Since the development of data from a particular population or sample of a population is typically limited in scope, we develop a trend that is regarded as a "best fit" function based upon an averaging of the data. Interpretation of the trend may ...

#### Solution Summary

This solution discusses regression analysis of data. In regression analysis, data is used to determine a matching mathematical function that best approximates the data. A graphic of a "best curve" matched to data is attached.

Statistics Questions: regression, predictor variables, plot data, exponential trend

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!

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