Is it defense or offense that wins football games? Consider the following portion of data, which includes a team's winning record (Win in %), the average number of yards gained, and the average number of yards allowed during the $2009$ NFL season.

$$\begin{array}{|l|c|c|c|} \hline \text { Team } & \text { Win } & \text { Yards Gained } & \text { Yards Allowed } \\ \hline \text { Arizona Cardinals } & 62.50 & 344.40 & 346.40 \\ \hline \text { Atlanta Falcons } & 56.30 & 340.40 & 348.90 \\ \hline \vdots & \vdots & \vdots & \vdots \\ \hline \text { Washington Redskins } & 25.00 & 312.50 & 319.70 \\ \hline \end{array}$$

a. Compare two simple linear regression models, where Model 1 predicts the winning percentage based on Yards Gained and Model 2 uses Yards Allowed.

b. Estimate a multiple linear regression model, Model 3, that applies both Yards Gained and Yards Allowed to forecast the winning percentage. Is this model an improvement over the other two models? Explain.

The accompanying data file shows the square footage and associated property taxes for 20 homes in an affluent suburb 30 miles outside New York City.

a. Estimate a home's property taxes as a linear function of the size of the home (measured by its square footage).

b. What proportion of the sample variation in property taxes is explained by the home's size?

c. What proportion of the sample variation in property taxes is unexplained by the home's size?

Choose the best answer. When people order books from a popular online source, they are shipped in standard-sized boxes. Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pounds, the mean weight of the packing material is 0.5 pounds with a standard deviation of 0.1 pounds, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source? (a) 1.84 (b) 2.60 (c) 3.02 (d) 3.40 (e) 9.10

The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for $20$ used sedans.

$$\begin{array}{|c|c|c|} \hline \text { Selling Price } & \text { Age } & \text { Mileage } \\ \hline 13590 & 6 & 61485 \\ \hline 13775 & 6 & 54344 \\ \hline \vdots & \vdots & \vdots \\ \hline 11988 & 8 & 42408 \\ \hline \end{array}$$

Predict the selling price of a five-year-old sedan with $65,000$ miles.

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $\$ 1,000$ s). He collects data on 20 individuals. A portion of the data is as follows:

$$\begin{array}{|c|c|} \hline \text { Salary } & \text { Education } \\ \hline 40 & 3 \\ \hline 53 & 4 \\ \hline \vdots & \vdots \\ \hline 38 & 0 \\ \hline \end{array}$$

What is the predicted salary for an individual who completed $7$ years of higher education?

The accompanying table shows a portion of data consisting of the selling price, the age, and the mileage for $20$ used sedans.

$$\begin{array}{|c|c|c|} \hline \text { Selling Price } & \text { Age } & \text { Mileage } \\ \hline 13590 & 6 & 61485 \\ \hline 13775 & 6 & 54344 \\ \hline \vdots & \vdots & \vdots \\ \hline 11988 & 8 & 42408 \\ \hline \end{array}$$

Interpret the slope coefficient of Age.

Choose the best answer. An agronomist wants to test three different types of fertilizer (A, B, and C) on the yield of a new variety of wheat. The yield will be measured in bushels per acre. Six 1-acre plots of land were randomly assigned to each of the three fertilizers. The treatment, experimental unit, and response variable are, respectively, (a) a specific fertilizer, bushels per acre, a plot of land. (b) a plot of land, bushels per acre, a specific fertilizer. (c) random assignment, a plot of land, wheat yield. (d) a specific fertilizer, a plot of land, wheat yield. (e) a specific fertilizer, the agronomist, wheat yield.

An agronomist used four test plots to determine the relationship between the wheat yield y (in bushels per acre) and the amount of fertilizer x (in pounds per acre). The results are shown in the table.

$$\begin{array}{|c|c|c|c|c|} \hline \text { Fertilizer, x} & {100} & {150} & {200} & {250} \\ \hline \text { Yield, y} & {35} & {44} & {50} & {56} \\ \hline \end{array}$$

(a) Use the regression capabilities of a graphing utility to find the least squares regression line for the data. (b) Use the model to approximate the wheat yield for a fertilizer application of 175 pounds per acre.

The country with a literacy rate of 49% is closest to which of the following percentiles? (a) 6th (b) 10th (c) 28th (d) 49th (e) There is not enough information to calculate the percentile.

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $\$ 1,000$ s). He collects data on 20 individuals. A portion of the data is as follows:

$$\begin{array}{|c|c|} \hline \text { Salary } & \text { Education } \\ \hline 40 & 3 \\ \hline 53 & 4 \\ \hline \vdots & \vdots \\ \hline 38 & 0 \\ \hline \end{array}$$

Interpret the coefficient for Education.

For a sample of $41 \mathrm{New}$ England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $\$ 1,000$ s). He finds that $S S E=4,182,663$ and $S S T=7,732,451$.

b. What proportion of the sample variation in crime rate is explained by the variability in the explanatory variables? What proportion is unexplained?

For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $\$ 1,000$ s). He finds that $S S E=4,182,663$ and $S S T=7,732,451$.

a. Calculate the standard error of the estimate.

b. What proportion of the sample variation in crime rate is explained by the variability in the explanatory variables? What proportion is unexplained?

Healthy living has always been an important goal for any society. In a recent ad campaign for Walt Disney, First Lady Michelle Obama shows parents and children that eating well and exercising can also be fun (USA Today, September 30, 2010). Consider a regression model that conjectures that fruits and vegetables and regular exercising have a positive effect on health and smoking has a negative effect on health. The sample consists of the percentage of these variables observed in various states in the United States in 2009. A portion of the data is shown in the accompanying table.

$$\begin{array}{|c|c|c|c|c|} \hline \text { State } & \begin{array}{c} \text { Healthy } \\ (\%) \end{array} & \begin{array}{c} \text { Fruits/Vegetables } \\ (\%) \end{array} & \begin{array}{c} \text { Exercise } \\ (\%) \end{array} & \begin{array}{c} \text { Smoke } \\ (\%) \end{array} \\ \hline \text { AK } & 88.7 & 23.3 & 60.6 & 14.6 \\ \hline \text { AL } & 78.3 & 20.3 & 41 & 16.4 \\ \hline \vdots & \vdots & \vdots & \vdots & \vdots \\ \hline \text { WY } & 87.5 & 23.3 & 57.2 & 15.2 \\ \hline \end{array}$$

a. Estimate the model Healthy $=\beta_0+\beta_1$ Fruits/ Vegetables $+\beta_2$ Exercise $+\beta_3$ Smoke $+\varepsilon$.

b. Analyze the data to determine if multicollinearity and changing variability are present.

Healthy living has always been an important goal for any society. In an ad campaign for Walt Disney, former First Lady Michelle Obama shows parents and children that eating well and exercising can also be fun (USA Today, September 30,2010 ). Consider a regression model that conjectures that fruits and vegetables and regular exercising have a positive effect on health and smoking has a negative effect on health. The sample consists of the percentage of these variables observed in various states in the United States in 2009. A portion of the data is shown in the accompanying table.