Question

Construct a 95% confidence interval estimate of the population slope. 9. Construct a 95% confidence interval estimate of the mean monthly rental for all onebedroom apartments that have 800 square feet in size. 10. Construct a 95% prediction interval of the monthly rental for an individual one-bedroom apartment that is 800 square feet in size.

Answer 1

An agent for a residential real estate company 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 48 one-bedroom apartments and collects and stores a data in dataset RentSilverSpring (can be found in both editions of datasets on the Blackboard). 7. At the 0.05 level of significance, is there an evidence of a linear relationship between the size of the apartment and the monthly rent? 8. Construct a 95% confidence interval estimate of the population slope. 9. Construct a 95% confidence interval estimate of the mean monthly rental for all onebedroom apartments that have 800 square feet in size. 10. Construct a 95% prediction interval of the monthly rental for an individual one-bedroom apartment that is 800 square feet in size

see explanation

Explanation:

`H_0 : \beta_1 = 0\\H_A : \beta_1 \\eq 0`

Rejection rule

If p = value
`\leq \alpha (= 0.05),` then reject the null hypothesis
`H_0`

Using Excel (Mega stat in Adds-in) procedure

Step 1 ; Choose Mega Stat > Correlation/Regression > Regression Analysis

Step 2 ; Select input ranges, enter the variable as column of X, independent Variable(s) and eneter the variable as the column of Y, Dependent Variabe

Step 3; Chect the appropriate option in options. Enter 800 in preditor values

Step 4 ; Click Ok

The Value of the test statistics is t = 2.570

Therefore by rejection rule , reject the null hypothesis
`H_0`

There is sufficient evidence at level of significance
`\alpha = 0.05`

There is significant linear relationship between the size of the apartment and monthly rent

(8) The 95% confidence interval estimate of the population slope is
`0.1069 < \beta_1 < 0.8795`

(9) The 95% confidence interval estimate of the mean monthly rent for all one bedroom apartment that are 800 square feet in size is (1330.7500, 1444.2990)

(10) The 95% predition interval estimate of the mean monthly rental for all one bedroom apartment that are 800 square feet in size is (1008.7666, 1766.2860).