Use the standard error to construct an approximate prediction interval for $Y$. Based on the width of this prediction interval, would you say the predictions are good enough to have practical value?

Construct the indicated prediction interval and interpret the results.

Construct a 95% prediction interval for the proceeds from initial public offerings in the ten questions back when the number of offerings is 200.

Construct the indicated prediction interval and interpret the results.

The total assets in equity funds is $900 billion. Construct a prediction interval for the total assets in bond and income funds. Use the results of Exercise 16 and c = 0.90.

Construct the indicated prediction interval and interpret the results.

When the voting age population is 210 million, construct a 99% prediction interval for the voter turnout in federal elections. Use the results of Exercise 16.

Perform the regression and write the estimated regression equation (round off to 3 or 4 significant digits for clarity). Do the coefficient signs agree with your $a$ priori expectations?

Perform the regression and write the estimated regression equation (round off to 3 or 4 significant digits for clarity). Do the coefficient signs agree with your a priori expectations?

Using the "Metals" data, construct a correlation matrix of the six independent variables. The response variable is Price/lb. (a) Identify any pairs of independent variables that have a significant pairwise correlation. (b) Using MegaStat or MINITAB, run the regression with all six predictor variables, calculating the VIF for each predictor. (c) Did you see any cause for concern based on the VIF values? Why or why not?

An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 25 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was $1.17$ bushels. Find the approximate width of a 95 percent prediction interval for wheat yield, assuming that the predictor values for a test plot are near the means of the sample predictors. Would the quick rule give similar results?

Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub-Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics.

(a) Write the regression model, being careful to exclude the base indicator variable.

(b) Find the $p$-value for each coefficient, using 319 degrees of freedom. Using an $\alpha = .01$, which predictor variable(s) are not significant predictors?

(c) By how much does the natural log of refrigerator price decrease from a two-door, side freezer model to a two-door, top freezer model?

(d) Which model demands a higher price: the side freezer or the one door with freezer model?

How many criterion variables are there in a multiple-regression analysis? How many predictor variables?

An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 25 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.17 bushels. Find the approximate width of a 95 percent prediction interval for wheat yield, assuming that the predictor values for a test plot are near the means of the sample predictors. Would the quick rule give similar results?

Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub-Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics. (a) Write the regression model, being careful to exclude the base indicator variable. (b) Find the p-value for each coefficient, using 319 degrees of freedom. Using an $\alpha=.01$, which predictor variable(s) are not significant predictors? (c) By how much does the natural log of refrigerator price decrease from a two door, side freezer model to a two door, top freezer model? (d) Which model demands a higher price: the side freezer or the one door with freezer model?

$$\begin{array}{lccr} \hline \text { Variable } & \text { Coefficient } & \text { Standard Error } & \boldsymbol{t} \text { Statistic } \\ \hline \text { Intercept } & 5.484092 & 0.13081309 & 41.923 \\ \text { Sale price } & -0.0733 & 0.02338826 & -3.134 \\ \text { Sub-Zero brand } & 1.11962 & 0.14615699 & 7.660 \\ \text { Total capacity (in cubic ft) } & 0.06956 & 0.00535103 & 12.999 \\ \text { Two door, freezer on bottom } & 0.046569 & 0.0808569 & 0.576 \\ \text { Two door, side freezer } & \text { Base } & & \\ \text { Two door, freezer on top } & -0.343246 & 0.03595873 & -9.546 \\ \text { One door with freezer } & -0.709558 & 0.13097047 & -5.418 \\ \text { One door, no freezer } & -0.881981 & 0.14913992 & -5.914 \\ \hline \end{array}$$

A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: $X_1$ = median age in 2005, $X_2$ = number of 2005 bank- ruptcies, $X_3$ = 2004 federal expenditures per capita (a leading predictor), and $X_4$ = 2005 high school graduation percentage.

(a) Calculate the t statistic for each coefficient to test for $\beta_j$ = 0.

(b) Look up the critical value of Student’s t in Appendix D for a two-tailed test at $\alpha$ =.01. Which coefficients differ significantly from zero?

(c) Use Excel to find a $p$-value for each coefficient.

Perform the regression and write the estimated regression equation (round off to 3 or 4 significant digits for clarity). Do the coefficient signs agree with your a priori expectations?