You may need to use the appropriate technology to answer this question. The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained. Analysis of Variance SOURCE DF Adj SS Regression 1 41587.3 Error 7 Total 8 51984.1 Predictor Coef SE Coef T-Value Constant 20.000 3.2213 6.21 X 7.210 1.3626 5.29 Regression Equation Y = 20.0 + 7.21 X (a) How many apartment buildings were in the sample? (b) Write the estimated regression equation. ŷ = (c) What is the value of sb1? (d) Use the F statistic to test the significance of the relationship at a 0.05 level of significance. State the null and alternative hypotheses. H0: ????1 ≠ 0 Ha: ????1 = 0 H0: ????0 ≠ 0 Ha: ????0 = 0 H0: ????1 = 0 Ha: ????1 ≠ 0 H0: ????0 = 0 Ha: ????0 ≠ 0 H0: ????1 ≥ 0 Ha: ????1 < 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Reject H0. We conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant. Reject H0. We cannot conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant. Do not reject H0. We conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant. Do not reject H0. We cannot conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant. (e) Predict the selling price (in thousands of dollars) of an apartment building with gross annual rents of $65,000.

(d) we do not reject the null hypothesis and cannot conclude that the relationship between selling price and annual gross rents is significant.

(e) selling price of an apartment building with annual gross rents of $65,000 would be [tex]ŷ = 20.0 + 7.21x = 20.0 + 7.21(65) = $517.35[/tex]

What is regression analysis?

A mathematical method for determining the average association between two or more variables in terms of the original units of the data is regression analysis.

(a) There were 8 apartment buildings in the sample, as indicated by the value of DF in the ANOVA table.

(b) The estimated regression equation is [tex]ŷ = 20.0 + 7.21x[/tex], where x is the annual gross rents (in thousands of dollars) and ŷ is the predicted selling price (in thousands of dollars).

(c) The value of sb1 is 1.3626, which is the standard error of the slope estimate.

(d) The null hypothesis for the test is that the relationship between selling price and annual gross rents is not significant, or H0: β1 = 0. The alternative hypothesis is that the relationship is significant, or Ha: β1 ≠ 0.

The F statistic for the test is calculated as follows:

F = (sb1² / s²)

= (1.3626² / 7983.6) = 0.17

The p-value for the test can be calculated using the F distribution with 1 and 7 degrees of freedom. The p-value is 0.68, which is greater than the significance level of 0.05.

Therefore, we do not reject the null hypothesis and cannot conclude that the relationship between selling price and annual gross rents is significant.

(e) To predict the selling price of an apartment building with annual gross rents of $65,000, we can use the estimated regression equation: [tex]ŷ = 20.0 + 7.21x = 20.0 + 7.21(65) = $517.35[/tex] (in thousands of dollars).

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