1. QUESTION 1 A real estate agency is interested in determining the number of houses that will be sold in a given quarter. The management of the agency believes that a relationship can be found between the number of houses sold (Y), the listed price (X1) and the current interest rates (X2). Their past experience shows that they tend to have better luck using a non-linear relationship. Below is the output from a regression analysis using the natural logarithm of the explanatory variables (but not of the dependent variable) in the model. Summary measures Multiple R R-Square Adj R-Square StErr of Estimate 0.9326 0.8698 0.8498 0.0259 ANOVA Table Source Explained Unexplained df 2 13 SS 0.0581 0.0087 MS 0.0290 0.0007 F 43.4187 Coefficient 4.3965 -0.8255 -0.1225 Std Err 0.7549 0.2467 0.1880 t-value 5.8239 3.3456 -0.6512 p-value 0.0001 0.0053 0.5262 p-value 0.0000 Regression coefficients Constant Log Price Log Interest 2. 3. Which of the following interpretations of the regression coefficients is correct? a If the listed price increases by $1, sales decrease by 0.8255 houses. . b If the interest rate increases by 1%, sales decrease by 0.1225, given that prices . remain constant. c If the interest rate increases by 1% while holding price constant, sales decrease by . 12.25%. d If price increases by 1%, sales decrease by 0.008255, given that interest rates . remained unchanged. 1. QUESTION 2 A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: Y^ = 84 +7X. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is $140. True False 1. 2. An express delivery service company recently conducted a study to investigate the relationship between the cost of shipping a package (Y), the package weight(X1), and the distance shipped (X2) . Twenty packages were randomly selected from among the large number received for shipment, and a detailed analysis of the shipping cost was conducted for each package. The data is attached in the data file below: Homework 6 Data.xlsx (The link to the data file won't work in Microsoft Edge - use a different browser.) Estimate a simple linear regression model involving shipping cost and distance shipped. Interpret the slope coefficient of the least squares line. a As the distance increases by one mile, the shipping cost increases by $1.49 on . average. b For every additional mile the package is shipped, shipping costs increase by $0.04 all . other things equal. c For every additional dollar spent, you can ship the package an additional 0.04 miles. . d We cannot determine this effect with this regression as the results are insignificant. . 1. QUESTION 4 Add the other explanatory variable - package weight - to the regression from the previous question. Estimate this expanded model. Based on your results, which model would you choose? a The results in the expanded model are more significant than in the first model. Therefore we should choose . the second model. b The first model has a higher coefficient for the distance shipped variable, therefore it should be chosen to . fully account for this factor. c The R squared in the expanded model are higher than in the first model. Therefore it fits the data better and . we should choose the expanded model. d Both R squared and adjusted R squared in the expanded model are higher than in the first model. Therefore . it fits the data better and we should choose the expanded model