Question

Heat Power is a utility company that would like to predict the monthly heating bill for a household in a particular region during the month of January. A random sample of 18 households in the region were selected and their January heating bill recorded. The 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 (Type: heat pump = 1 or natural gas = 0). Household 2 3 4 5 6 7 8 9 10 11 12 13 Bill $255 $286 $296 $300 $305 $317 $321 S321 $339 $349 $369 $374 $381 $413 $419 $441 $522 $560 SF 2.070 1.909 2.004 2.307 3,021 2.683 1.511 2.836 2.553 2.497 2.103 2.486 2.279 2,477 3.218 3,080 2.507 3,517 Age 7 17 8 22 5 14 8 3 20 11 12 18 19 17 11 8 20 18 Type Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Natural Gas Heat Pump Ileat Pump Heat Pump Heat Pump Heat Pump Heat Pump Heat Pump Heat Pump 15 16 17 18

Answer 1

1)

Answer:

($368.528, $457.781)

Explanation:

The regression equation is defined as,

$\widehat{\text{Bill}}=144.72+0.0583\text{ SF}+2.4157\text{ Age}+95.0806\text{ Type}$

For SF = 2600, Age = 9, Type = 1

Bill = 144.72 + 0.0583 x 2600+ 2.4157 x 9 + 95.0806 x 1

$\widehat{\text{Bill}}=413.1128$

The 95% confidence interval is obtained using the following formula,

$\text{95\% CI}=\widehat{Y} \pm \text{ME}$

where $\widehat{Y} =$ predicted monthly heating bill, the margin of Error (ME) = 44.62688

Now,

$\text{95\% CI}=413.1228\pm 44.62688$

$\text{95\% CI}=(368.496,457.750)$

2)

Answer:

($307.19, $519.11)

Explanation:

The 95% prediction interval is obtained using the following formula,

$\text{95\% PI}=\widehat{Y} \pm \text{ME}$

where $\widehat{Y} =$ predicted monthly heating bill, the margin of Error (ME) = 105.9601

Now,

$\text{95\% PI}=413.1228\pm 105.9601$

$\text{95\% PI}=(307.16,519.08)$