Question

A regression analysis is performed using data for 36 single-family homes to predict appraised value​ (in thousands of​ dollars) based on land area of the property​ (in acres), X1i​, and age​ (in years), X2i​, in month i. Use the results below to complete parts​ (a) and​ (b) below.

Variable	Coefficient	Standard Error	t Statistic	​p-value
Intercept	392.60372	51.68272	7.60	0.0000
​ Area, X1	451.43475	100.48497	4.49	0.0001
​ Age,X2	−2.17162	0.79077	−2.75	0.0097

a. Construct a​ 95% confidence interval estimate of the population slope between appraised value and land area.

_____ ≤ β1≤ _____

b. At the 0.05 level of​ significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these​ results, indicate the independent variables to include in this model. Choose the correct hypotheses for X1 below.

Choose the correct hypotheses for X2 below.

O A. Ho: B1 #1 H4: B1 = 1 O C. Ho: B1 = 0 H: B170 OB. Ho: B4 = 1 HY:B181 OD. Ho: B1 * 0 H4: B1 = 0 Find the test statistic. tstat = (Round to two decimal places as needed.) Determine the p-value. p-value = (Round to four decimal places as needed.) Reach a conclusion. Choose the correct answer below. V Ho. There sufficient evidence that X, makes a significant contribution to the regression model.

On the basis of these​ results, indicate the independent variables to include in this model. Choose the correct answer below.

A.Include both variables X1 and X2.

B.Include neither variable X1 nor variable X2.

C.Include only the variable X1.

D.Include only the variable X 2.

Answer 1

Answer Date: 11/11/2019 a) A 95% confidence interval estimate of the population slope between appraised value and land area is, First, compute the t critical value then find confidence interval. The t critical value is, The sample size is small and two-tailed test. Look in the column headed a=0.05 and the row headed in the t distribution table by using degree of freedom is, d.f. = n-2 = 36-2 = 34 The t critical value is 2.032.

95% C.I. = Parameter estimate Ft. Standard error of parameter estimate = 451.43475 + 2.032x100.48497 = 451.43475 + 204.21003 = 247.22472 to 655.64478 A 95% confidence interval estimate of the population slope between appraised value and land area is 247.22472 to 655.64478 - b) To test the hypothesis is that the slop of land area (X1) makes a significant contribution to the regression model at 5% significance level. The null and alternative hypothesis is, Ho:B, = 0 H.:B, 70 The answer is C.

The t-test statistics is, From Computer output, the t-test statistics is 4.49). The p-value for this test is, From Computer output, the p-value for this test is 0.0001). Decision The conclusion is that the p-value in this context is less than 0.05 which is 0.0001, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the slop of land area (X1) makes a significant contribution to the regression model. The result is statistically significant. To test the hypothesis is that the slop of age (X2) makes a significant contribution to the regression model at 5% significance level. The null and alternative hypothesis is, H.:B2 = 0 H2:32 +0

The answer is D The t-test statistics is, From Computer output, the t-test statistics is -2.75. The p-value for this test is, From Computer output, the p-value for this test is 0.0097). Decision The conclusion is that the p-value in this context is less than 0.05 which is 0.0097, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the slop of age (X2) makes a significant contribution to the regression model. The result is statistically significant. On the basis of these results, land area (x1) and age (X2) include in the independent variables in this model due to each land area (X1) and age (X2) independent variable is significant.