An agent for a residential real estate company in a large city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:

Size (square feet)	Rent ($)
850	1950
1450	2600
1085	2200
1232	2500
718	1950
1485	2700
1136	2650
726	1935
700	1875
956	2150
1100	2400
1285	2650
1985	3300
1369	2800
1175	2400
1225	2450
1245	2100
1259	2700
1150	2200
896	2150
1361	2600
1040	2650
755	2200
1000	1800
1200	2750

 

For these data, S_yx = 194.5953946 and h_i = 0.049156908 when X = 1000.  *Round final answers below to three decimal places.  Do not round calculations until the final answer.

(a) Construct a 95% confidence interval estimate of the mean monthly rental for all apartments that are 1000 square feet in size.

(b) Construct a 95% prediction interval of the monthly rent for an individual apartment that is 1000 square feet in size.

(c) Explain the difference in the results in (a) and (b).