Basic Business Statistics Concepts and Applications by Mark Berenson, David Levine, Kathryn Szabat, David Stephan Textbook Question

Question

problem 13.47). In Problem 13.9 on page 494, an agent for a real estate company wanted to predict the monthly rent for one-bedroom apartments, based on the size of the apartment. The data are stored in RentSilverSpring . Use the results of that problem.

a. At the 0.05 level of significance, is there evidence of a linear relationship between the size of the apartment and the monthly rent?

b. Construct a 95% confidence interval estimate of the population slope, b1.

Answer 1

I don't have access to specific data or the textbook you mentioned, but I can guide you on how to perform the hypothesis test and construct a confidence interval for the population slope (b1) based on linear regression analysis. You can follow these general steps using statistical software or a calculator:

a. Hypothesis Test for Linear Relationship:

1. Null Hypothesis (H0): There is no linear relationship between the size of the apartment and the monthly rent (b1 = 0).
2. Alternative Hypothesis (Ha): There is a linear relationship between the size of the apartment and the monthly rent (b1 ≠ 0).

To test this hypothesis at the 0.05 level of significance, you will need to perform a t-test for the regression coefficient b1. The steps include:

1. Fit a linear regression model using the data from RentSilverSpring.
2. Obtain the t-statistic for the slope (b1) and its associated p-value.
3. Compare the p-value to the significance level (0.05) to make a decision.

If the p-value is less than 0.05, you would reject the null hypothesis, indicating evidence of a linear relationship.

b. Confidence Interval for Population Slope (b1): To construct a 95% confidence interval for the population slope (b1), you can use the following formula:

Confidence Interval: b1 ± t*(standard error of b1)

1. Calculate the standard error of b1 from the regression output.
2. Find the t-critical value for a 95% confidence level (usually around 1.96 for a large sample size).
3. Plug these values into the formula to calculate the confidence interval.

Remember to use the regression output from the analysis you conducted in Problem 13.9 on page 494 to obtain the necessary statistics, including the estimate of b1 and its standard error. These steps will allow you to answer part (a) by conducting a hypothesis test and part (b) by constructing a confidence interval for the population slope.