For following fitted trend, make a prediction for period $t$ = 17:

$y_t$ = $2286e^{.076t}$

(a) Plot the voter participation rate.

(b) Describe the trend (if any) and discuss possible causes.

(c) Fit both a linear and a quadratic trend to the data.

(d) Which model is preferred? Why?

(e) Make a forecast for 2012, using a trend model of your choice (or a judgment forecast).

(f) If possible, check the web for the actual 2012 voter participation rate. How close was your forecast?

Note: Time is in 4-year increments, so use $t$ = 16 for the 2012 forecast.

Name an advantage and a disadvantage of each method.

Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars), $X_1$ = display floor space (square meters), $X_2$ = competitors’ advertising expenditures (thousands of dollars), $X_3$ = advertised price (dollars per unit).

(a) Calculate the t statistic for each coefficient to test for $\beta$ = 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 the $p$-value for each coefficient.

Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y= total sales (thousands of dollars), $X_1=$ display floor space (square meters), $X_2=$ competitors' advertising expenditures (thousands of dollars), $X_3=$ advertised price (dollars per unit). (a) Calculate the t statistic for each coefficient to test for $\beta=0$. (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 the p-value for each coefficient.

$$\begin{array}{lcc} \hline \text { Predictor } & \text { Coefficient } & \text { SE } \\ \hline \text { Intercept } & 1225.4 & 397.3 \\ \text { FloorSpace } & 11.522 & 1.330 \\ \text { CompetingAds } & -6.935 & 3.905 \\ \text { Price } & -0.14955 & 0.08927 \\ \hline \end{array}$$

A regression model to predict the price of diamonds included the following predictor variables: the weight of the stone (in carats where 1 carat = 0.2 gram), the color rating (D, E, F, G, H, or I), and the clarity rating (IF, VVS1, VVS2, VS1, or VS2).

(a) Identify the quantitative predictor variable(s).

(b) How many indicator variables would be included in the model in order to prevent the least squares estimation from failing?

(c) Write the proposed model form for predicting a diamond price.

A regression model to predict the price of diamonds included the following predictor variables: the weight of the stone (in carats where 1 carat $=0.2$ grams), the color rating (D, E, F, G, H, or I), and the clarity rating (IF, VVS1, VVS2, VS1, or VS2). (a) Identify the quantitative predictor variable(s). (b) How many indicator variables would be included in the model in order to prevent the least squares estimation from failing? (c) Write the proposed model form for predicting a diamond price.

Hotel guest satisfaction. Each year, J. D. Power and Associates publishes the results of its North American Hotel Guest Satisfaction Index Study. For 2015, the study revealed that $15 \%$ of hotel guests were "delighted" with their experience (giving a rating of 10 out of 10). Among these guests, $80 \%$ stated they would "definitely" recommend the hotel. In a random sample of 15 hotel guests, consider the number $(x)$ of guests who were delighted with their stay and would recommend the hotel. Use the rules of probability to determine the value of $p$ for this binomial experiment.

Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y = total sales (thousands of dollars), $X_1$ = display floor space (square meters), $X_2$ = competitors’ advertising expenditures (thousands of dollars), $X_3$ = advertised price (dollars per unit).

(a) Write the fitted regression equation.

(b) Interpret each coefficient.

(c) Would the intercept seem to have meaning in this regression?

(d) Make a prediction for Sales when FloorSpace = 80, CompetingAds = 100, and Price = 1,200.

Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y= total sales (thousands of dollars), $X_1=$ display floor space (square meters), $X_2=$ competitors" advertising expenditures (thousands of dollars), $X_3=$ advertised price (dollars per unit). (a) Write the fitted regression equation. (b) Interpret each coefficient. (c) Would the intercept seem to have meaning in this regression? (d) Make a prediction for Sales when FloorSpace =80, CompetingAds =100, and Price =1,200.

$$\begin{array}{lc} \hline \text { Predictor } & \text { Coefficient } \\ \hline \text { Intercept } & 1225.44 \\ \text { FloorSpace } & 11.52 \\ \text { CompetingAds } & -6.935 \\ \text { Price } & -0.1496 \\ \hline \end{array}$$

Refer to the U.S. defense budget outlay regression estimated in Exercise 7.18.

a. Comment generally on the estimated regression results.

b. Set up the ANOVA table and test the hypothesis that all the partial slope coefficients are zero.

Refer to the ANOVA table for this regression.

(a) State the degrees of freedom for the F test for overall significance.

(b) Use Appendix F to look up the critical value of F for $\alpha=.05$.

(c) Calculate the F statistic. Is the regression significant overall?

(d) Calculate $R^2$ and $R_{\mathrm{adj}}^2$, showing your formulas clearly.

$$\begin{array}{lrrr} \hline \text { Source } & \text { d.f. } & {\text { SS }} & {\text { MS }} \\ \hline \text { Regression } & 3 & 1,196,410 & 398,803 \\ \text { Error } & 26 & 379,332 & 14,590 \\ \quad \text { Total } & 29 & 1,575,742 & \\ \hline \end{array}$$

Refer to the ANOVA table for this regression.

(a) State the degrees of freedom for the F test for overall significance.

(b) Use Appendix F to look up the critical value of F for $\alpha=.05$.

(c) Calculate the F statistic. Is the regression significant overall?

(d) Calculate $R^2$ and $R_{\mathrm{adj}}^2$, showing your formulas clearly.

$$\begin{array}{lccr} \hline \text { Source } & \text { d.f. } & \text { SS } & \text { MS } \\ \hline \text { Regression } & 4 & 259,412 & 64,853 \\ \text { Error } & 45 & 224,539 & 4,990 \\ \quad \text { Total } & 49 & 483,951 & \\ \hline \end{array}$$

Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was $Y=$ total sales (thousands of dollars), $X_1=$ display floor space (square meters), $X_2=$ competitors' advertising expenditures (thousands of dollars), $X_3=$ advertised price (dollars per unit). (a) Write the fitted regression equation. (b) Interpret each coefficient. (c) Would the intercept seem to have meaning in this regression? (d) Make a prediction for Sales when FloorSpace $=80$, CompetingAds $=100$, and Price $=1,200$.

As in bivariate regression, there is one residual for every observation in a multiple regression:

$$e_i=y_i-\hat{y}_i \quad \text { for } i=1,2, \ldots, n$$