Part $1($LO $2\mathrm{.}1)$:

$-$ Client $1$: Client $1$ is moving to Northampton from another city, and is interested in whether the number of bedrooms, number of full bathrooms, number of square feet, number of rooms, walk friendliness $($measured by walk score$),$ and being in Northampton $($as opposed to Florence, MA$,$ which is adjacent$)$ impact the price of the house. If a variable impacts the price of a house, the client would like to know how much the impact is$.$

$-$ You have the following regression output:

$1.$ Identify which variables are statistically significant determinants of the price of a house.

$2.$ What percent of the variation in house price is explained by the variables in this model?

$3.$ Write down the sign of the coefficient $($positive or negative$)$ and describe the magnitude, i$.$e$.,$ if $\backslash ($ x $\backslash )$ goes up by one unit, how much does the price of the house change by$?$

$4.$ Now pretend that you were Client $1$ and that you've looked at the variables in the data dictionary. Are there any other variables you think would impact the price of the house?

Part $2($LO $2\mathrm{.}2)$:

$-$ Client $2$: Client $2$ has a house in Northampton. She owns a three bedroom, two bathroom house that is $2,000$ square feet with a garage on $\mathrm{.}5$ acre of land. Prior to selling her house, she is considering building an addition to her house with one extra bedroom and one half bath that would add about $300$ square feet to her house. She would like to know how much the price of the house might change as a result.

$1.$ Write down the regression model that you need to estimate to help Client $2.$

$2.$ Estimate the model in Excel. Print out the output: you can highlight the regression output, click Print Selection, then click Scale to Fit to get it on one page.

$3.$ Write down the estimated model with the estimated values of the coefficients.

$4.$ Plug in the values of the house that she owns to predict the current value of her house. Then plug in the values of the renovated house to get the estimated value of the renovation.

$5.$ Do you think she should do the renovation? Why or why not?