Question

A real estate agent would like to know if the number of bedrooms in a house can be used to predict the selling price of the house. More specifically, she wants to know whether a larger number of bedrooms leads to a higher selling price. Records for 25 houses that recently sold in the area were selected at random, and data on the number of bedrooms (x) and the selling price (y) (in $000s) for each house were used to fit the model E(y) = β0 + β1x.

The value of the test statistic for testing β1 is 11.3383 and the corresponding standard error is 1.29384. What is the linear relationship between bedrooms and the selling price?

Answer 1

Solution: We are given the test statistic for testing is 11.3383 and standard error of is 1.29384.

From the given information, we can find the estimate of

rounded to two decimal places.

The positive sign of suggests that there is a positive linear relationship between bedrooms and the selling price.

Now we need to find the t critical value at 0.05 significance level for df = 23 in order to find whether there is a significant linear relationship between the bedrooms and the selling price.

The t critical value is:

Since the test statistic of is greater than the t critical value, we, therefore, reject the null hypothesis and conclude there exists a positive linear relationship between the bedrooms and the selling price.