A Realtor, is analyzing the relationship between the sale price of a home (Price in \$), its square footage ( $ qqt), 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 =0+1 Sqft +2 Beds +3 Baths +4 Colonial +. 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 $16,651, all else constant. For each additional bedroom in a house, the average price of a house is expected to decreases by $16,651, all else constant. As the price of a house increases by $16,651, the house is expected to have one less bedroom, all else constant. As the price of a house increases by $16,651, the house is expected to have one more bedroom, all else constant. b-2. Interpret the coemicient of colonial. All eise constant, the price of a colonial-style house is, on average, $34,844 less than a non-Colonial style. All else constant, the price of o colonial-style house is, on average, $34,814 more than a non-Colonial style. Al else constant, the price of a colonial-style house is, on average, $33,206 less than a non-Colonial style. All eise constant, the price of a colonial-style house is, on average, $33,206 more 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 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. \begin{tabular}{|c|c|c|c|c|c|} \hline 1 & Price & Sqft & Beds & Baths & Colonial \\ \hline 2 & 812000 & 2961 & 1 & 2.5 & 0 \\ \hline 3 & 867000 & 2618 & 1 & 1.5 & 0 \\ \hline 4 & 760000 & 2545 & 4 & 3.0 & 1 \\ \hline 5 & 669000 & 2142 & 4 & 2.5 & 1 \\ \hline 6 & 699000 & 2547 & 2 & 2.0 & 0 \\ \hline 7 & 658000 & 2633 & 4 & 1.5 & 1 \\ \hline 8 & 644000 & 2505 & 4 & 1.5 & 0 \\ \hline 9 & 640000 & 2265 & 3 & 2.5 & 1 \\ \hline 10 & 616000 & 2028 & 1 & 2.5 & 0 \\ \hline 11 & 556000 & 1834 & 2 & 1.5 & 0 \\ \hline 12 & 551000 & 2434 & 1 & 2.5 & 1 \\ \hline 13 & 618000 & 3403 & 1 & 1.0 & 0 \\ \hline 14 & 596000 & 1652 & 3 & 2.0 & 0 \\ \hline 15 & 555000 & 1710 & 3 & 2.5 & 0 \\ \hline 16 & 521000 & 2755 & 1 & 2.5 & 1 \\ \hline 17 & 468000 & 1776 & 1 & 1.0 & 0 \\ \hline 18 & 474000 & 1935 & 2 & 1.5 & 0 \\ \hline 19 & 556000 & 1490 & 4 & 3.0 & 0 \\ \hline 20 & 459000 & 1624 & 4 & 2.0 & 1 \\ \hline 21 & 434000 & 1723 & 4 & 2.0 & 0 \\ \hline 22 & 473000 & 1786 & 1 & 3.0 & 0 \\ \hline 23 & 450000 & 1565 & 1 & 3.0 & 1 \\ \hline 24 & 403000 & 1612 & 4 & 2.5 & 1 \\ \hline 25 & 440000 & 1947 & 2 & 1.5 & 1 \\ \hline 26 & 398000 & 1228 & 4 & 1.5 & 1 \\ \hline 27 & 417000 & 1151 & 4 & 2.0 & 0 \\ \hline 28 & 443000 & 1178 & 4 & 2.0 & 0 \\ \hline 29 & 378000 & 1376 & 1 & 2.0 & 1 \\ \hline 30 & 383000 & 1025 & 4 & 2.0 & 1 \\ \hline 31 & 424000 & 2410 & 4 & 1.0 & 0 \\ \hline 32 & 366000 & 1113 & 2 & 2.0 & 0 \\ \hline 33 & 399000 & 1426 & 4 & 1.0 & 1 \\ \hline 34 & 343000 & 1610 & 2 & 3.0 & 0 \\ \hline 35 & 324000 & 1586 & 2 & 1.0 & 0 \\ \hline 36 & 344000 & 1368 & 2 & 2.0 & 0 \\ \hline 37 & 292000 & 677 & 2 & 1.0 & 0 \\ \hline 20 & 1.0 & 1.5 & 1 \\ \hline \end{tabular}