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

Describe which patterns of temporal precedence are indicated by different cross-lag correlational 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?

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?

When is an outlier most likely to be problematic?

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 bankruptcies, $X_3$= 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.

$$\begin{array}{lrr} \hline \text { Predictor } & \text { Coefficient } & {\text { SE }} \\ \hline \text { Intercept } & 4,198.5808 & 799.3395 \\ \text { AgeMed } & -27.3540 & 12.5687 \\ \text { Bankrupt } & 17.4893 & 12.4033 \\ \text { FedSpend } & -0.0124 & 0.0176 \\ \text { HSGrad\% } & -29.0314 & 7.1268 \\ \hline \end{array}$$

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.

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 below.

(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 $R^2_{adj}$, showing your formulas clearly.

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.

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

Refer to the ANONA table below. (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 $R_{\text {adj }}^2$, showing your formulas clearly.

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

Refer to the ANOVA table below. (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 $R_{\text {adj}}$ showing your formulas clearly.

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

Refer to the ANOVA table below.

(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 $R^2_{adj}$ , showing your formulas clearly.

Refer to the ANOVA table below.

(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 $R^2_{adj}$, showing your formulas clearly.