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.

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

The accompanying data file shows the square footage and associated property taxes for 20 homes in an affluent suburb 30 miles outside of New York City. Estimate a home's property taxes as a linear function of its square footage. At the $5 \%$ significance level, is square footage significant in explaining property taxes? Show the relevant steps of the test.

Caterpillar manufactures heavy machinery and equipment and provides financing for purchases by its customers. Caterpillar reported sales and interest revenues of $51,324 million for Year 1. The balance sheet showed current and noncurrent receivables of$15,752 million at the beginning of Year 1 and $18,448 million at the end of Year 1. Compute the amount of cash collected from customers during Year 1.

A realtor in Mission Viejo, California, believes that the average price of a house is more than $\$ 500,000$.

c. At $\alpha=0.05$, what is the conclusion to the test? Is the realtor's claim supported by the data?

Clear fractions or decimals, solve, and check. \

$$1.7 t+8-1.62 t=0.4 t-0.32+8$$

A realtor in Mission Viejo, California, believes that the median price of a house is more than $\$ 500,000$.

a. Specify the competing hypotheses for the test.

b. Using the $\boldsymbol{M} \boldsymbol{V}_{-}$Houses data, calculate the value of the test statistic. Assume the normal approximation for $T$.

c. Calculate the $p$-value.

d. At the $5 \%$ significance level, is the realtor's claim supported by the data?

The following table shows a portion of the monthly returns data (in percent) for 2010-2016 for two of Vanguard's mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund.

$$\begin{array}{|c|c|c|} \hline \text { Date } & \text { Energy } & \text { Healthcare } \\ \hline \text { Jan-10 } & -4.86 & -0.13 \\ \hline \text { Feb-10 } & 1.50 & 0.58 \\ \hline \vdots & \vdots & \vdots \\ \hline \text { Dec-16 } & -0.30 & -5.26 \\ \hline \end{array}$$

c. At the $5 \%$ significance level, what is the conclusion to the test? Are the returns on the mutual funds correlated?

The following table shows a portion of the monthly returns data (in percent) for 2010–2016 for two of Vanguard’s mutual funds: the Vanguard Energy Fund and the Vanguard Healthcare Fund.

$$\begin{array}{|c|c|c|} \hline \text { Date } & \text { Energy } & \text { Healthcare } \\ \hline \text { Jan-10 } & -4.86 & -0.13 \\ \hline \text { Feb-10 } & 1.50 & 0.58 \\ \hline \vdots & \vdots & \vdots \\ \hline \text { Dec-16 } & -0.30 & -5.26 \\ \hline \end{array}$$

The accompanying data file shows the square footage and associated property taxes for 20 homes in an affluent suburb 30 miles outside of New York City. Estimate a home's property taxes as a linear function of its size. At the 5% significance level, do home size and property taxes have a linear relationship? Show the relevant steps of the test.

The SAT has gone through many revisions over the years. People argue that female students generally do worse on math tests but better on writing tests. Consider the following portion of data on 20 students who took the SAT test last year. Information includes each student's score on the writing and math sections of the exam, the student's GPA, and a Female dummy variable that equals 1 if the student is female, 0 otherwise.

$$\begin{array}{|c|c|c|c|} \hline \text { Writing } & \text { Math } & \text { GPA } & \text { Female } \\ \hline 620 & 600 & 3.44 & 0 \\ \hline 570 & 550 & 3.04 & 0 \\ \hline \vdots & \vdots & \vdots & \vdots \\ \hline 540 & 520 & 2.84 & 0 \\ \hline \end{array}$$

a. Estimate a linear regression model with Writing as the response variable and GPA and Female as the explanatory variables.

b. Compute the predicted writing score for a male student with a GPA of 3.5. Repeat the computation for a female student.

c. At the $5 \%$ significance level, determine if there is a difference in writing scores between males and females.

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.

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.

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

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

a. Estimate the sample regression equation that enables us to predict the price of a sedan on the basis of its age and mileage.

b. Interpret the slope coefficient of Age.

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

Education reform is one of the most hotly debated subjects on both state and national policy makers' list of socioeconomic topics. Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio in $\%$, (2) TSAL is the average teacher's salary in $\$ 1,000 \mathrm{~s},(3) \mathbb{N C}$ is the median household income in $\$ 1,000$ s, and (4) SGL is the percentage of single-parent households. A portion of the data is shown in the accompanying table.

$$\begin{array}{|c|c|c|c|c|} \hline \text { Score } & \text { STR } & \text { TSAL } & \text { INC } & \text { SGL } \\ \hline 227.00 & 19.00 & 44.01 & 48.89 & 4.70 \\ \hline 230.67 & 17.90 & 40.17 & 43.91 & 4.60 \\ \hline \vdots & \vdots & \vdots & \vdots & \vdots \\ \hline 230.67 & 19.20 & 44.79 & 47.64 & 5.10 \\ \hline \end{array}$$

d. What is the predicted score if everything else is the same as in part (c) except INC $=$ $80 ?$