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% prediction interval to estimate the cost in February to heat a Northeast home that is3,100 square feet.

Heating_Cost_($)   Square_Footage
340   2440
280   2440
290   2020
250   2210
300   2320
440   2610
320   2230
380   3120
320   2520
360   2910

Explanation / Answer

Model is:

attach(HOME)
mod <- lm(Heatingcost~ Squarefootage,data=HOME)

Output:

coefficients:
Estimate Std. Error t value
(Intercept) 57.54946 110.46205 0.521
Squarefootage 0.10896 0.04415 2.468
Pr(>|t|)
(Intercept) 0.6165
Squarefootage 0.0388 *

Reg eq is heatingcost=57.55+0.10896(squarefootage)

To predict:

newdata = data.frame(Squarefootage=3100)
predict(mod, newdata, interval="predict",level=.90)

Output:

fit lwr upr
1 395.3402 295.8101 494.8704

a 90% prediction interval to estimate the cost in February to heat a Northeast home that is3,100 square feet. is

295.8101 and 494.8704

lower limit=295.8101

upper limit=494.8704

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