Instructions: Regardless of what the book says, please do not solve any of the problems by hand. Use the computer to obtain all answers.

3. For each of the data sets discussed in this section, use a computer to access the data, construct a scatterplot of \(y\) versus \(x\), and produce the regression output relating \(y\) to \(x\).

1. Estimating Residential Real Estate Values: The file name is REALEST3.
2. Pricing Communications Nodes: The file name is COMNODE3.
3. Forecasting Housing Starts: The file name is HSTARTS3.

5. Central Company (continued) Refer to Exercise 2.

1. Test the hypotheses \(H_{0}: \beta_{1}=0\) versus \(H_{a}: \beta_{1} \neq 0\) at the \(5 \%\) level of significance. State the decision rule, the test statistic value and your decision.
2. From the result in part a, are hours of labor and number of items linearly related?
3. Test the hypotheses \(H_{a}: \beta_{0}=0\) versus \(H_{a}: \beta_{0} \neq 0\) at the \(5 \%\) level of significance State the decision rule, the test statistic value and your decision.
4. From the result in part c, what can be concluded?

6. Dividends A random sample of 42 firms was chosen from the S&P 500 firms listed in the Spring 2003 Special Issue of Business Week (TT= Business Week Fifty Best Performers). The dividend yield (DIV YIELD) and the 2002 earning 7er share (EPS) were recorded for these 42 firms. These data are in a file named DIV3.

Using dividend yield as the dependent variable and EPS as the independent variable, a regression was run. Use the results to answer the questions. The scatterplot of DIVYIELD and EPS shown in Figure 3.19. The regression results are sown in Figure 3.20.

1. What is the sample regression equation relating dividends to EPS?
2. Is there a linear relationship between dividend yield and EPS? Use \(\alpha=0.05\). State the hypotheses to be tested, the decision rule, the test statistic, and your decision.
3. What conclusion can be drawn from the test result?
4. Construct a \(95 \%\) confidence interval estimate of \(\beta_{1}\)
5. Construct a \(95 \%\) confidence interval estimate of \(\beta_{0}\).

10. Dividends (continued) Use the regression res in Figure 3.20 to help answer the questions

1. What percentage of the variation in dividend yield has been explained by the regression
2. Use the \(F\) test to test the hypotheses \(H_{0}: \beta_{1}=0\) versus \(H_{a}: \beta_{1} \neq 0\) at the \(5 \%\) level of significance. Be sure to state the decision rule, the test statistic value, and decision.

11. Sales/Advertising (continued) Use the regression results in Figure 3.22 to help answer the questions.

1. What percentage of the variation in sales has been explained by the regression?
2. Use the \(F\) test to test the hypotheses \(H_{0}: \beta_{1}=0\) versus \(H_{a}: \beta_{1} \neq 0\) at the \(5 \%\) level of significance. Be sure to state the decision rule, the test statistic value, and your decision.

*Figure 3.22, which is needed to solve #11, is below.

14. Dividends (continued), Consider the dividend yield problem in Exercise 6 and the associated computer results in Figure 3.20. An analyst wants an estimate of dividend yield for all firms with earnings per share of $ 3. Does the equation developed provide a more accurate estimate than simply using the sample mean dividend yield for all 42 firms examined? State why or why not.

15. Sales/Advertising (continued), Use the results in Figure 3.33 to help solve these problems. These results were obtained requesting a prediction with \(x=200,250,300\) and 350 , respectively (representing $\$ 20,000, \$ 25,000, \$ 30,000$ and \(\\) 35,000)$.

1. Find an estimate of average sales for all sales districts with advertising expenditures of $\$ 25,000$. Find a point estimate and a \(95 \%\) confidence interval estimate.
2. Predict sales for individual districts having advertising expenditures of $\$ 20,000, \$ 25,000$, $\$ 30,000$, and $\$ 35,000$. Find point predictions as well as \(95 \%\) prediction intervals.

*Figure 3.33, which is needed to solve #15, is below.

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