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.

Click here for the Excel Data File

a$.$ Estimate the model: Price $=\backslash$beta $0+\backslash$beta $1$Sqft $+\backslash$beta $2$Beds $+\backslash$beta $3$Baths $+\backslash$beta $4$Colonial $+\backslash$epsi $.$

Note: Negative values should be indicated by a minus sign. Round Coefficients to $2$ decimal places.

b$-1.$ Interpret the coefficient of beds.

multiple choice $1$

For each additional bedroom in a house, the average price of a house is expected to increases by $$32,979,$ all else constant.

For each additional bedroom in a house, the average price of a house is expected to decreases by $$32,979,$ all else constant.

As the price of a house increases by $$32,979,$ the house is expected to have one less bedroom, all else constant.

As the price of a house increases by $$32,979,$ the house is expected to have one more bedroom, all else constant.

b$-2.$ Interpret the coefficient of colonial.

multiple choice $2$

All else constant, the price of a colonial$-$style house is$,$ on average, $$10,516$ less than a non$-$Colonial style.

All else constant, the price of a colonial$-$style house is$,$ on average, $$10,516$ more than a non$-$Colonial style.

All else constant, the price of a colonial$-$style house is$,$ on average, $$71,726$ less than a non$-$Colonial style.

All else constant, the price of a colonial$-$style house is$,$ on average, $$71,726$ 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 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.