Asking Price Fireplace ($000) Size (sq. ft.) Coded 452.1 1423 941.8 2990 Question 2. (66 points) A group of researchers would like to study how different factors influence the sellers of 623.8 2936 house to determine their asking price (in thousand dollars). They include two factors: house size (meausred by 409.6 1439 square feet) and whether the house has the fire place (which is a dummy variable coded as 1 if there is a fireplace and 1879.8 5602 as 0 otheriwse). A random sample of 30 houses was selected, with the results given in the table. 936.0 2191 843.8 2798 a. State the multiple regression equation. 700.3 2070 b. Interpret the meaning of the two slopes in this problem. 516.6 2710 c. Predict the mean selling price for a house with 2000 square feet but without a fireplace. 488.0 1416 d. Perform a residual analysis on the results (please construct the residual plot on house size, 885.9 3244 the residual plot on predicted values of Y variable, and normal probability plot on residual) and 872.7 2493 determine the adequacy of the model. 963.6 3335 e. Is there a significant relationship between selling price and the two independent variables altogether 614.3 1968 (house size and fireplace) at the 0.05 level of significance? Please provide the details of the test, 940.7 3136 including hypothesis, test statistic, decision rule, and conclusion. 697.4 2194 f. At the 0.05 level of significance, does the house size significantly affect selling price of house, 681.8 3032 holding constant the effect of having a fireplace or not? Please provide the details of the test, 523.9 1970 including hypothesis, test statistic, decision rule, and conclusion. 1116.2 3356 g. At the 0.05 level of significance, does having a fireplace make a difference for selling price of house, 506.8 2070 holding constant the effect of the house size? Please provide the details of the test, including 820.0 2826 hypothesis, test statistic, decision rule, and conclusion. Having a fireplace or having no fireplace has a 491.2 1606 higher house price? 740.3 2063 h. Based on your answer to the above questions (f) and (g), determine what independent variable(s) should 335.5 1392 be included in the regression model. 407.4 1120 i. Construct a 95% confidence interval estimate of the population slope for the relationship between selling 392.8 1817 price and house size. 474.2 2496 j. Compute and interpret the meaning of 535.7 1615 k. Compute and interpret the meaning of the adjusted . 480.4 1788 1140.4 3130