Question

An agent for a real estate company in a large city collected data on the sizes​ (x in square​ feet) and monthly rents​ (y in​ dollars) of a sample of eight apartments in a neighborhood. The data is shown​ below, along with the linear regression equation. Complete parts a through c below.

yi = 279.7 + 0.906 xi

Monthly Rent ($)	900	1500	800	1,600	1,950	950	1,750	1,350
Size​ (Square Feet)	800	1,300	1,050	1,250	2,000	700	1,300	1,050

a. Estimate the mean monthly rent for an apartment that has​ 1,000 square feet.

The mean monthly rent for such an apartment is approximately $__________

​(Round to the nearest cent as​ needed.)

b. Interpret the coefficients b0 and b1 in this problem. is the answer a , b , c or d ?

A. For each increase of 1 square foot in​ space, the monthly rent is expected to increase by $279.7 Since X cannot be​ zero, 0.906 has no practical interpretation.

B. For each increase of 1 square foot in​ space, the monthly rent is expected to increase by $279.7. Apartments in this neighborhood cost at least $0.906.

C. For each increase of 1 square foot in​ space, the monthly rent is expected to increase by $0.906. Since X cannot be​ zero, 279.7 has no practical interpretation.

D. For each increase of 1 square foot in​ space, the monthly rent is expected to increase by $0.906. Apartments in this neighborhood cost at least $279.7.

c. You have been asked to estimate the mean monthly rent for an apartment that has​ 2,500 square feet. Discuss how you would proceed and indicate your cautions. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your answer. Pick a,b, c or d

A.The estimated mean monthly rent is___, as long as b1 is greater than 0.

​(Round to two decimal places as​ needed.)

B. It is not appropriate for the linear regression equation to estimate this​ value, because the value is greater than 2 standard deviations from the mean apartment size.

C. The correlation between an​ apartment's size and its monthly rent is too weak to use this model for such a prediction.

D. It is not appropriate for the linear regression equation to estimate this​ value, because the value is outside the range of values given for apartment size.

Answer 1

Solution-A:

we have yi = 279.7 + 0.906 xi

for xi=1000

yi=279.7 + 0.906 *1000

=  1185.70

1185.70

Solution-b:

slope=0.906

Fro unit increase in size ,monthly rent increases by 0.906 units

y intercept=279.7 is when x (rent)=0

practically has no meaning for y intercept

For each increase of 1 square foot in​ space, the monthly rent is expected to increase by $0.906. Since X cannot be​ zero, 279.7 has no practical interpretation.

Solution-c:

2500 is out of range

we need to extrapolate

D. It is not appropriate for the linear regression equation to estimate this​ value, because the value is outside the range of values given for apartment size.