A quantitatively savvy, young couple is interested in purchasing a home in northern New York. They collected data on $48$ houses that had recently sold in the area. They want to predict the selling price of homes $($in thousands of dollars$)$ based on the size of the home $($in square feet$).$

The regression equation is Price $($in thousands$)=17\mathrm{.}1+0\mathrm{.}0643$ Size $($sq$.$ ft$.)$

Predictor

Coef

SE Coef

T

P

Constant

$17\mathrm{.}06$

$24\mathrm{.}59$

$0\mathrm{.}69$

$0\mathrm{.}491$

Size $($sq$.$ ft$.)$

$0\mathrm{.}06427$

$0\mathrm{.}01224$

$5\mathrm{.}25$

$0\mathrm{.}000$

S $=48\mathrm{.}5733$ R$-$Sq $=37\mathrm{.}5\%$ R$-$Sq$($adj$)=36\mathrm{.}1\%$

Predicted Values for New Observations

Size $($sq$.$ ft$.)$

Fit

SE Fit

$95\%$ CI

$95\%$ PI

$2000$

$145\mathrm{.}61$

$7\mathrm{.}07$

$(131\mathrm{.}38,159\mathrm{.}83)$

$(46\mathrm{.}80,244\mathrm{.}41)$

Use the computer output to provide and interpret a $95\%$ interval for the selling price of a single $2,000$ square foot house in this portion of northern New York.

A quantitatively savvy, young couple is interested in purchasing a home in northern New York. They collected data on $48$ houses that had recently sold in the area. They want to predict the selling price of homes $($in thousands of dollars$)$ based on the size of the home $($in square feet$).$

The regression equation is Price $($in thousands$)=17\mathrm{.}1+0\mathrm{.}0643$ Size $($sq$.$ ft$.)$

Predictor

Coef

SE Coef

T

P

Constant

$17\mathrm{.}06$

$24\mathrm{.}59$

$0\mathrm{.}69$

$0\mathrm{.}491$

Size $($sq$.$ ft$.)$

$0\mathrm{.}06427$

$0\mathrm{.}01224$

$5\mathrm{.}25$

$0\mathrm{.}000$

S $=48\mathrm{.}5733$ R$-$Sq $=37\mathrm{.}5\%$ R$-$Sq$($adj$)=36\mathrm{.}1\%$

Predicted Values for New Observations

Size $($sq$.$ ft$.)$

Fit

SE Fit

$95\%$ CI

$95\%$ PI

$2000$

$145\mathrm{.}61$

$7\mathrm{.}07$

$(131\mathrm{.}38,159\mathrm{.}83)$

$(46\mathrm{.}80,244\mathrm{.}41)$

Use the computer output to provide and interpret a $95\%$ interval for the selling price of a single $2,000$ square foot house in this portion of northern New York.

PI: $(46\mathrm{.}80,244\mathrm{.}41)$

We are $95\%$ sure that the selling price of a $2,000$ square foot house in this portion of northern New York is between $$46,800$ and $$244,410.$

CI: $(131\mathrm{.}38,159\mathrm{.}83)$

We are $95\%$ sure that the selling price of a $2,000$ square foot house in this portion of northern New York is between $$131,380$ and $$159,830.$

PI: $(46\mathrm{.}80,244\mathrm{.}41)$

We are $95\%$ sure that the mean selling price of all $2,000$ square foot houses in this portion of northern New York is between $$46,800$ and $$244,410.$

CI: $(131\mathrm{.}38,159\mathrm{.}83)$

We are $95\%$ sure that the mean selling price of all $2,000$ square foot houses in this portion of northern New York is between $$131,380$ and $$159,830.$