A realtor is interested in developing a model that describes the relationship between the square feet in an apartment and the monthly rent. A random sample from 32 apartments in Saint Petersburg was analyzed. The minimum square feet was 650, the maximum was 1150. The correlation coefficient was 0.344, with a two-sided p-value = 0.323. The least squares regression equation treating square feet as the independent variable was y = 2.47x - 340.5.

(a) Interpret the slope if appropriate. Select the correct answer below:
A. For each additional square foot, the rent will be $2.47 more per month.
B. For each additional $100 per month in rent, the apartment will have 247 more square feet.
C. For each additional square foot, the rent will be $347.50 less per month.
D. It is not appropriate to provide an interpretation of the slope; there is not a statistically significant linear correlation between the two variables.

The problem presented involves understanding the relationship between the size of an apartment in square feet and the monthly rent, using a least squares regression model. The least squares regression equation given is [tex]y = 2.47x - 340.5[/tex], where:

[tex]y[/tex] represents the monthly rent.
[tex]x[/tex] is the square footage of the apartment.

Interpretation of the Slope

The slope of the line in a regression equation represents the rate of change in the dependent variable (rent) for a one-unit increase in the independent variable (square feet).

Here, the slope is [tex]2.47[/tex], which means:

A. For each additional square foot, the rent will be $2.47 more per month.

This is the correct interpretation of the slope. Therefore, the chosen answer is A.

Evaluation of Significance

While interpreting this slope is mathematically correct, we must consider statistical significance. The correlation coefficient is 0.344, which implies a weak positive linear relationship. The p-value is 0.323, which is greater than the common significance level of 0.05.

This high p-value indicates that the linear relationship captured by the regression model is not statistically significant at the 5% level. While it is appropriate to mathematically interpret the slope, one should be cautious about drawing conclusions in practical settings because the statistical evidence suggesting a meaningful linear relationship is weak.

In conclusion, the slope interpretation is correct, but the lack of statistical significance should be noted when considering the real-world applicability of this model.