# RES/342 Week 5 Answer Guide - Statistics

Chapter 12 -Chapter Exercises 12.48 and 12.50

Chapter 13 - Chapter Exercises 13.30

Chapter 14 - Chapter Exercise 14.16

**Problem 12.48**

*In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two- tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.*

a. Y = 0.0343x + 30.7963

b. Degrees of Freedom = 33, and Critical Value = 2.035

c. The data seems to show that the slope does not equal 0. Since the p-value is greater than .05 this would lead me to reject the null hypothesis.

d. 95% Confidence Interval.

Upper Limit = 0.058

Lower Limit = 0.010

e. t2 = 2.8892**
**t2 = 8.34632

Yes, it fits.

f. There is not a very good fit to this regression because the majority of the variation of X cannot be accounted for by Y. This leads me to the conclusion that there are other factors and this is not a good linear fit.

**Problem 12.50**

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, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that

*F*=

*t*2 for the slope. (f) In your own words, describe the fit of this regression.

a. Y = 0.0452X + 6.5763

b. Degrees of Freedom = 63 and Critical Value = 5.291

c. The slope does equal 0, and the p-value is greater than .05 so we are able to accept the bull hypothesis.

d. 95% Confidence Interval.

Upper Limit = 0.056

Lower Limit = 0.034

e. t2 = 8.1832

**t2 = 66.961**

Yes, it fits.

f. This regression fits well because variation of X can be expianed for over 50% of Y. This means that the majority of the variation is accounted for.

**Problem 13.30**

*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 kilometer), GDPCap (Gross Domestic Product per capita), and Literate (literacy percent). Interpret these results.*

Interpretation: The next aspect of this test that stands out is the high value of R^2. This leads me to the conclusion that the slopes of these variables pair well and account for any significant variation. This shows us that there is a strong level of correlation between the dependent variables. Also, the p-values for GDPcap and Literacy are very low. This leads me to believe that literacy levels amount to a lower infant mortality rate and a higher GDP per capital also has a positive impact.

**Problem 14.16**

*(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?*

a.

b. The plot does not follow a normal patter. This makes it difficult to track the patter and make a sensible conclusion about the trend of the data.

c. A fitted plot would not be very helpful because the data does not follow a set pattern A fitted plot would leave the data in the same situation we are currently in.

f. It is bet to ignore the earlier years data because the airline industry is changing rapidly. In this case, a time series analysis would not be the ideal choice of a test to make a prediction about future results.

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