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A Realtor, is analyzing the relationship between the sale price of a home (Price in \$), its square footage (Sqft), the number of bedrooms (Beds), the number of bathrooms (Baths), and a Colonial dummy variable (Colonial equals 1 if a colonial-style home, 0 otherwise). The accompanying data file shows information on 36 recent home sales. a. Estimate the model: Price \( =\beta_{0}+\beta_{1} \mathrm{Sqft}+\beta_{2} \) Beds \( +\beta_{3} \) Baths \( +\beta_{4} \) Colonial \( +\varepsilon \) : Note: Negative values should be indicated by a minus sign. Round Coefficients to 2 decimal places. b-1. Interpret the coefficient of beds. For each additional bedroom in a house, the average price of a house is expected to increases by \( \$ 827 \), all else constant. For each additional bedroom in a house, the average price of a house is expected to decreases by \( \$ 827 \), all eise constant. As the price of a house increases by \( \$ 827 \), the house is expected to have one more bedroom, all else constant. As the price of a house increases by \( \$ 827 \), the house is expected to have one less bedroom, all else constant. b-2. Interpret the coefficient of coloniai.
b-2. Interpret the coefficient of colonial. All else constant, the price of a colonial-style house is, on average, \( \$ 23,342 \) more than a non-Colonial style. All else constant, the price of a colonial-style house is, on average, \( \$ 23,342 \) less than a non-Colonial style. All else constant, the price of a colonial-style house is, on average, \( \$ 206,526 \) more than a non-Colonial style. All else constant, the price of a colonial-style house is, on average, \( \$ 206,526 \) less than a non-Colonial style house. c. Construct the \( 95 \% \) confidence interval for expected price for a 2,500-square-foot, colonial-style home with three bedrooms and two bathrooms. Note: Round final answers to the nearest whole number. d. Construct the \( 95 \% \) prediction interval for price for a 2,500-square-foot, colonial-style home with three bedrooms and two bathrooms. Note: Round final answers to the nearest whole number.

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