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 2,300 square feet. EEB Click the icon to view the data table. Determine the upper and lower limits of the confidence interval. UCL-$ LCL $ Round to two decimal places as needed.) Sre E Heating Square Heating Cost) Footage Cost () Footage 350 2,430 460 280 2,450 320 2,250 310 2,020 390 3,140 260 2,250 330 2,540 320 2,350 380 2,920 Print Done

Answer 1

Answer)

First, we need to find the line of regression

which is equal to

Y = a + r*(sy/sx)*X

where y is = cost

sy = standard deviation for cost

and sx is the standard deviation for square feet

mean of y = 340

mean of x 2496

sy = 58.1187

sx = 330.797

r = 0.6143468459939

Y = a + 0.6143468459939*(58.1187/330.797)*X

Y = a + 0.1079364082451*X

a = mean of y - (mean of x * 0.1079364082451)

a = 70.432

Y = 70.432 + 0.108*X

now we need to find the standard deviation for this we will calculate the predicted value of price then we will subtract the predicted value from the actual price and will take the square,

2 80 324.213 596.7/ 3 52-312| 167-681 | 23 192 5 9 가요.crl pie -332 -872 892 S 96 CamScainer

s.d = 48.64

margin of error = t*(s.d/square root of n)

n is = 10

degrees of freedom is = n-2 = 8

for df 8 and confidence level of 90

t = 1.86

margin of error(MOE) = 28.61

Now we need to find the predicted value for 2300 square feet

Y = 70.432 + 2300*0.108 = 318.832

confidence interval:

UCL = 318.832 - 28.61 = 290.22

LCL = 318.832 + 28.61 = 347.44