Suppose a government department would like to investigate the relationship betwe

Question

Suppose a government department would like to investigate the relationship between the cost of heating a home during the month of February in the Northeast and the home's square footage. The accompanying data set shows a random sample of 10 homes. Construct a 90% confidence interval to estimate the average cost in February to heat a Northeast home that is 2, 700 square feet. Click the icon to view the data table. Determine the upper and lower limits of the confidence interval. UCL = $ LCL = $ (Round to two decimal places as needed.)

Explanation / Answer

The correlation between Heating Cost (Y) and Square Footage (X) is 0.66 and simple linear regression can be written as,

Y=bo+b1*X+E

The OLS estimate of bo and b1 are 61.9 and 0.11 respectively. Thus, the confidance interval of average Y for given X=Xo is

(Ypre-t (alpha/2,n-2) sqrt(MSres(1/n+((Xo-E(x))^2/sum((X-E(X))^2))),

(Ypre+t (alpha/2,n-2) sqrt(MSres(1/n+((Xo-E(x))^2/sum((X-E(X))^2))),

i. e. (318.99,398.81)

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