In the dataset "duke_forest_for_homework.xlsx", we have the following seven columns/variables for a dataset gathered from Zillow in November of 2020 for listed homes in the Duke Forest neighborhood of Durham, North Carolina:

Column name	Description
Price ($1000s)	Price of the house (in $1000s)
Bath	Number of bathrooms
Area	Area of the house (in square feet)
Lot	House lot size (in acres)
Central_cooling	1 if the house has central cooling and 0 if not
Bed	Number of bedrooms
Heat_pump	1 if the house has a heat pump and 0 if not

1. You are interested in buying a house in the Duke Forest neighborhood and one of your friends tells you that the only thing that matters for a house price is the lot size. Run a regression with price as the response/dependent (Y) variable and lot size as the only independent/predictor (X) variable. Please paste the output here:
2. According to the coefficients from this regression, what is the equation you would use to predict the price of a home?
3. How much of the variation in home price is explained by the variation in lot size, and which value from the output did you use to determine that?
4. If a house lot size decreases by 0.5 acres, what will be the change in home price according to this regression?