Question 1: Regression Analysis (8 Marks) A market research for real estate investments was carried on last year to reveal the sales figures of new houses of different prices. The estimated regression equation for these data is ? = 251.57 – 0.8 x. Price (Thousands of $) Xi 160 280 180 200 260 240 220 Sales of New Homes This Year Yi 125 20 104 85 40 80 75 Answer all the following questions: a) If the coefficient of determination for this example is 0.92, then find the correlation coefficient and comment on its value. (2 marks) b) What does the correlation coefficient tell you about the relationship between price and sales of new houses? (2 marks) c) Use the regression equation to predict the sales of new houses if the price is 180 thousand dollars. (2 marks) d) Use the regression equation to predict the price if the sales of new houses is 108 thousand. (2 marks)
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We are given the coefficient of determination, which is $R^2 = 0.92$. To find the correlation coefficient, we need to take the square root of the coefficient of determination and determine its sign. Since we don't have information about the direction of the Show more…
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Question 1 (Multiple Regression): We conduct a study to determine the determinants of house prices (in thousands of dollars) in Montreal. We run the following multiple regression model: House prices = ̠₀ + ̠₁(Areaሱ) + ̠₂(Number of Bedroomsሱ) + ̠₃(Year of Constructionሱ) + ̦ሱ The explanatory variables are: (i) Area, a dummy variable (where Downtown = 1, and Other = 0); (ii) Number of Bedrooms; and (iii) Year of Construction. We obtain a sample of 100 observations. We obtained the following results: ANOVA df SS MS Regression 3 5523.709 1841.57 Residual A 335.5119 3.505333 Total 99 5861.221 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 39.75415 31.3013 1.270048 0.207137 -22.3784 101.8867 Area B 0.374814 13.72036 0.000000 4.398583 5.886582 Year of Construction 0.03474 0.015665 2.2176 C 0.003644 0.065835 Number of Bedrooms 5.000415 0.133277 37.51899 0.000000 4.735863 D 1. (2 points) Find the value of A in the above table.
Madhur L.
4-16 Steve Caples, a real estate appraiser in Lake Charles, Louisiana, has developed a regression model to help appraise residential housing in the Lake Charles area. The model was developed using recently sold homes in a particular neighborhood. The price (Y) of the house is based on the square footage (X) of the house. The model is ˆ Y = 33,478 + 62.4X. The coefficient of correlation for the model is 0.63. Use the model to predict the selling price of a house that is 1,860 square feet. A house with 1,860 square feet recently sold for $165,000. Explain why this is not what the model predicted. If you were going to use multiple regression to develop an appraisal model, what other quantitative variables might be included in the model? What is the coefficient of determination for this model?
David N.
Text 1: You are given the following information about variables y and x: y x Dependent Variable Independent Variable -0.0 -7.2 8.2 3.7 -3.1 6.4 10.3 7.7 In addition, it is known that the slope of the regression line b1 = -2.6 The y-intercept b0 for the estimated regression equation equals ____ (round your answer to two decimal places). Text 2: Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained: y = 12 + 1.8x n = 25 sb1 = 0.2683 Using α = 10%, the critical t value for testing the significance of the slope is ____ Show your answer with three decimal places. Text 3: As a result of running a simple regression on a data set, the following estimated regression equation was obtained: y = 1.0 - 5.0x Furthermore, it is known that SSR = 760, and SSE = 131. Calculate the correlation coefficient R; round your answer to three decimal places.
Sri K.
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