Assignments from the E-Text

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W5- Assignments from the E-Text

Name: ______Total Points: = 4.0

The following assignments are taken from the E-text, AppliedStatistics in Business and Economics, by Doane and Seward

Instruction: Please provide complete answers to the parts shown below. For full credit, all Work Must Be Shown. Please submit as attachment to your individual forum under appropriate thread by midnight, (MST), Monday, Day (7) of Week Five.

Chapter 12:

Chapter Exercises 12.48 (1.0 point)

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

(a)Develop and State the fitted regression equation. ( 0.25 point)

y = 0.0343x + 30.7963

(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 ( 0.25 point)

Dof = 35 – 1 = 34, critical value of t corresponding to 34 dof at  = 0.05 (two-tailed) is 2.032.

(c)What is your conclusion about the slope? Use the appropriate value from the above table, and provide appropriate explanation! (0.25 point)

Since the p- value for the slope is 0.0068 (< 0.05) the weekly pay has a significant influence on the income tax withheld.

(d)Interpret the 95 percent confidence interval limits for the slope.Use the appropriate limits from the above table, and provide appropriate explanation! (0.25 point)

The 95% confidence interval for the slope is [0.0101, 0.0584]. This means we are 95% confident that the population slope lies between the above limits.

Chapter Exercises 13.32 (1.0 point)

13.32An 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.

Dependent variable: Year (Year in which the salary was observed)

Predictors:

YearHire (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. (0.25 point)

R^2 = 0.811 implies that about 81.1% of the variation in salary is explained by the predictor variables. R = 0.811 = 0.90 being a high value, the regression as a whole appears to be a strong fit.

(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. (0.25 point)

The p- values are 0 for all the three predictor variables. This indicates that all the three predictor variables have slopes different from 0 and their influence is significant.

(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? (0.25 point)

It matters, since the p- value for Race is 0

(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? (0.25 point)

An assistant professor earns less than a full professor. She earns $6438 less.

Chapter Exercises 14.16 (2 points)

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

(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 (0.50 point)

Data and Trend Graph:

(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. (0.50 point)

Data and Trend Graph:

(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. (0.75 point)

The exponential fit is y = 721.5 e^0.115x

For 2004, x = 13 and y = 721.5 e^0.115(13) = 3217.41 planes

By eyeballing the most recent data, the prediction for 2004 is about 2200 planes.

(d)In part (b), we choose a subset (1992-2003). Why is it best to ignore earlier years in this data set. Explain! (0.25 point)

On comparing the trend fitted first (1966 to 2003) and the latter one (1992 to 2003), it is clear that if the data prior to 1992 is ignored, we are in a position to have a reasonably linear trend line which can be used for future prediction. Hence, the data of the earlier years is best ignored. [Also note the increase in the value of R^2 from 0.614 to 0.756.]