Question

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).

Answer 1

Answer;-

Given That:-

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.

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

A 95% confidence interval estinate of the mean mpthly rental for all apartments that are 1000 square feet in size is

By using Excel software, find confidence interval with help of following steps:

1) import the data.

2) Select the MegaStat from Add-Ins option.

3) Select the Regression Analysis from Regression.

4) Select data input.

5) Enter predictor value from Predictor value from spreadsheet.

  

From the Excel output, a 95% confidence interval estimate of the mean monthly rental for all apartments that are 1000 square feet in size is 2153.014 to 2331.516.

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

A 95% prediction interval of the monthly rent for an individual apartment that is 1000 square feet in size is,

From excel output in part (a), a 95% prediction interval of the monthly rent for an individual apartment that is 1000 square feet in size is 1829.938 to 2654.591.

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

The difference in results in part(a) is suggest that there are 95% confident that the mean monthly rental for all apartments that are 1000 square feet in size is between 2153.014 and 2331.516 and part (b) is suggest that there are 95% chance (Probability) that the monthly rent for an individual apartment that is 1000 square feet in size is between 1829.938 and 2654.591.

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