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 2,800 square feet.

Heating_Cost_($)   Square_Footage
340   2420
290   2410
290   2010
270   2240
310   2330
450   2620
330   2230
400   3120
330   2530
380   2910

Explanation / Answer

We estimate a simple linear regression equation:

using excel add in

equation:

Heating cost=34.4+.123*Sqfeet

so for 2800 sqft

Heating cost=34.4+.123*2800=378.8

Now, prediction interval:

SE= SQRT[MSE*{1+1/n+(xh-x_mea)^2/(Sxx)}] ==SQRT(1675.14*(1+1/10+(2800-2482)^2/(10*98856))) = 44.89

t==T.INV.2T(0.1,9) = 1.83

Predictio interval= predicted value +- t*SE=

formula:

SUMMARY OUTPUT Regression Statistics Multiple R 0.725462 R Square 0.526294 Adjusted R Square 0.467081 Standard Error 40.92849 Observations 10 ANOVA df SS MS F Significance F Regression 1 14888.87 14888.87 8.888129 0.017566 Residual 8 13401.13 1675.141 Total 9 28290 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 34.39913 102.9871 0.334014 0.746956 -203.09 271.8878 -203.09 271.8878 0.122724 0.041165 2.981297 0.017566 0.027798 0.21765 0.027798 0.21765

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