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 ($) 850 1950 1450 2600 1085 2200 1232 2500 718 1950 1485 2700 1136 2650 726 1935 700 1875 956 2150 1100 2400 1285 2650 1985 3300 1369 2800 1175 2400 1225 2450 1245 2100 1259 2700 1150 2200 896 2150 1361 2600 1040 2650 755 2200 1000 1800 1200 2750 For these data, Syx = 194.5953946 and hi = 0.049156908 when X = 1000. *Round final answers below to three decimal places. Do not round calculations until the final answer. (a) Construct a 95% confidence interval estimate of the mean monthly rental for all apartments that are 1000 square feet in size. (b) Construct a 95% prediction interval of the monthly rent for an individual apartment that is 1000 square feet in size. (c) Explain the difference in the results in (a) and (b).
An agent for a residential real estate company in a large city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:
|
Size (square feet) |
Rent ($) |
|
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, Syx = 194.5953946 and hi = 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
(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).
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