Question

Consider Model 1 from Individual Assignment 2. Use this regression model to test (at the 5% level of significance) if the average price of a house in the East neighborhood is less than the average price of a similar house in the North neighborhood. StatTools Report Analysis: Regression Performed By: Bardossy Date: Friday, September 27, 2019 Updating: Static Variable Price Multiple Multiple Regression for Price Summary R-Square Rows Ignored Outliers Adjusted R-square 0.8578 Std. Err. of Estimate 50660.95358 0.9304 0.8656 0 0 Degrees of Freedom Sum of Squares Mean of Squares F p Value ANOVA TAW Explained <0.0001 1.98383E+12 2.83404E-11 110.4229223 3.07984E-11 2566532218 Unexplained 120 Coefficient Standard Error -Value P.Value 0 Regression Table Constant SqFt Bedrooms Bathrooms Offers Brick West East -12055 20512 44691.44115 -0.269743038 274.4720171 28.71182947 9.559544697 24088.33576 7944.589907 3.032042691 37363.03284 10792.47277 3.461952939 -40757.52654 5519. 172415 -7.384717032 85958.2151910054.72173 8.549039696 99685.9087215680.03715 6.357504628 -12020. 22191 12314.42924 -0.976108732 .7878 <0.0001 0.0030 0.0007 <0.0001 <0.0001 <0.0001 0.3310 Confidence interval 95% Lower Upper -100541.1483 76430.73805 217.624593 331.3194413 8358.600646 39818.07087 15994.68785 58731.37783 -51685. 103.82-29829.94927 66050.56593 105865.8645 68640.52643 130731.291 -36401.93479 12361.49096 A. State the null and alternative hypotheses. B. State the p-value for this test. C. State the statistical conclusion. D. Communicate the results of the test in "plain English" within the context of the problem.

Answer 1

A

Null Hypothesis: The average price of a house in the east neighborhood is less than the average price of a house in the north neighborhood.

Alternate Hypothesis: The average price of a house in the east neighborhood is greater than or equals to the average price of a house in the north neighborhood.

B

The p-value uses the calculated probability to determine whether there is sufficient evidence to reject the null hypothesis. Using the above ANOVA table, the p-value is less than 0.0001.

C

The level of significance (alpha) is 5% that is 0.05 which is greater than the p-value. Therefore, we reject the null hypothesis and conclude that the average price of a house in the east neighborhood is greater than or equals to the average price of a house in the north neighborhood.

D

Using part C, we reject the null hypothesis but for the final model, we will look at the p-value of the coefficients in the regression table. If the p-value of a variable is less than 0.05, then that variable is significant and should be kept in the final model. From the regression model, we have seen that except constant (intercept) and east, the rest of the variables are significant and should be kept in the final model.