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 2,100 square feet. Click the icon to view the data table Determine the upper and lower limits of the confidence interval UCL = $ Round to two decimal places as needed.)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Square Footage
Independent Variable: Heating Cost ($)
Square Footage = 1185.5836 + 3.9018568 Heating Cost ($)
Sample size: 10
R (correlation coefficient) = 0.65554387
R-sq = 0.42973776
Estimate of error standard deviation: 275.97996

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

90% confidence interval will be:

UCL = $ 14606.58

LCL = $ 4152.38

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 1185.5836 534.76356 0 8 2.2170238 0.0574 Slope 3.9018568 1.589139 0 8 2.4553276 0.0396

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