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psantiago psantiago
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3 weeks ago
Use the following information to answer the question(s) below.

Delmarva Power is a utility company that would like to predict the monthly heating bill for a household in Kent County during the month of January. A random sample of 18 households in the county were selected and their January heating bill recorded. This data is shown in the table below along with the square footage of the house (SF), the age of the heating system in years (Age,) and the type of heating system (heat pump = 1 or natural gas = 0).



Show the calculations for the test statistic for each regression coefficient for the heating bill model using α = 0.05 and interpret the results.
Textbook 

Business Statistics


Edition: 2nd
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hjhhjh
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df = n - k - 1 = 18 - 3 - 1 = 14
tα/2 = 2.145

SF variable:
H0β1 = 0
H1β1 ≠ 0
t =  =  = 2.47
Because  = 2.47 is greater than  = 2.145, we reject the null hypothesis. There is a significant relationship between the square footage of the household and the monthly heating bill.

Age variable:
H0β2 = 0
H1β2 ≠ 0
t =  =  = 1.20
Because   = 1.20 is less than  = 2.145, we fail to reject the null hypothesis. There is not a significant relationship between the age of the heating system in the house and the monthly heating bill.

Type variable:
H0β3 = 0
H1β3 ≠ 0
t =  =  = 3.84
Because   = 3.84 is greater than  = 2.145, we reject the null hypothesis. There is a difference in the average heating bill for a house with a natural gas system when compared to a house with a heat pump system.

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