AP Statistics Lesson 8.04 Problem A real estate agent is investigating a model to predict the selling price of homes in Virginia Beach. She takes a random sample of 39 current homes for sale and for each house, records the selling price of the home (in $1000), the living space (square footage) and whether or not the house is considered waterfront property. The scatter plot is shown below: Scatterplot of Price vs Size 1000 Waterfront no 900 yes 800 700 600 Price 500 400 300 200 100 1000 2000 3000 4000 5000 6000 Size Here is the regression analysis for all homes (no consideration of waterfront) Coefficients Term Coef SE Coef 95% CI T-Value P-Value VIF Constant 46.6 35.4 (-25.2, 118.4) 1.32 0.197 Size 0.1707 0.0138 (0.1428, 0.1986) 12.38 0.000 1.00 1. Write the linear model for the price of the home (in thousands of dollars) given the square footage. (2 points)2. Interpret the slope of the regression model in the context of the problem. (2 points) 3. Below are the regression models for the waterfront and non-waterfront homes. Fitted Line Plot Yes Price = 45.26 + 0.1741 Yes Size 1000 S 111.780 R-Sq 75.8% R-Sq(adj) 74.0% 900 800 700 600 Yes Price 500 400 300 200 100 1000 2000 3000 4000 5000 6000 Yes Size Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 45.3 74.3 0.61 0.552 Yes Size 0.1741 0.0263 6.62 0.000 1.00 Waterfront Homes (16 Homes)Fitted Line Plot No Price = 55.77 + 0.1642 No Size 900 S 60.8072 R-Sq 85.4% 800 R-Sq(adj) 84.7% 700 600 No Price 500 400 300 200 100 1000 2000 3000 4000 5000 No Size Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 55.8 35.4 1.58 0.130 No Size 0.1642 0.0148 11.06 0.000 1.00 Non-Waterfront Homes (23 Homes) Assume all conditions for inference have been met, calculate a 95% confidence interval for the slope of the regression line for both waterfront and non-waterfront homes: (4 points) Waterfront: Non-Waterfront:4. Using the regression models above, estimate the difference in price between a Waterfront 2000 ft2 home and a Non-Waterfront 2000 ft2 home. (2 points) 5. Assume all conditions for inference have been met, the 95% condence interval for the true difference between the two slopes (Waterfront - Non- Waterfront) is given below. Based on the interval, is there a signicant difference between the two slopes? Explain your reasoning. (2 points) Estimation for Difference Difference 95% CI for Difference 0.00990 (-0.00520. 0.02500)