A realtor wanted to find a model that re- NW lates the asking price of a...

  

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A realtor wanted to find a model that re- NW lates the asking price of a house to the square footage, num- ber of bedrooms, and number of baths. The following data are from houses in Greenville, South Carolina. Square Footage Bedrooms Baths Asking Price ($ thousands) 3,800 3.5 498 2,600 3 449 2,600 3.5 435 2,250 4 400 3,300 3 379 2,750 3 2.5 375 2,200 3 2.5 356 3,000 4 2.5 350 2,300 2 340 2,600 2.5 332 2,300 4 2 298 2,000 3 280 2,200 3 2.5 260 Source: remax.com (a) Construct the correlation matrix. Is there any reason to be concerned with multicollinearity? (b) Find the least-squares regression equation ŷ = bo+ bix + b₂x₂ + bts, where x₁ is square footage, x2₂ is number of bedrooms, x3 is number of baths, and y is the response variable "asking price." (c) Test Ho: B₁ B₂ B3 = 0 versus H₁: at least one of the B, 0 at the a= 0.05 level of significance. (d) Test the hypotheses Ho: B₁-0 versus H₁: B₁ 0, Ho: B₂0 versus H₁: B₂ 0, and Ho: B3 - 0 versus H₁: B30 at the a= 0.05 level of significance. (e) Remove the explanatory variable with the highest P-value and compute the least-squares regression equation. Are all the slope coefficients significantly different from zero? If not, remove the explanatory variable with the higher P-value and compute the least-squares regression equation. (1) Draw residual plots, a boxplot of the residuals, and a normal probability plot of the residuals to assess the adequacy of the model found in part (e). (g) Interpret the regression coefficients for the least-squares regression equation found in part (e). 3 A realtor wanted to find a model that re- NW lates the asking price of a house to the square footage, num- ber of bedrooms, and number of baths. The following data are from houses in Greenville, South Carolina. Square Footage Bedrooms Baths Asking Price ($ thousands) 3,800 3.5 498 2,600 3 449 2,600 3.5 435 2,250 4 400 3,300 3 379 2,750 3 2.5 375 2,200 3 2.5 356 3,000 4 2.5 350 2,300 2 340 2,600 2.5 332 2,300 4 2 298 2,000 3 280 2,200 3 2.5 260 Source: remax.com (a) Construct the correlation matrix. Is there any reason to be concerned with multicollinearity? (b) Find the least-squares regression equation ŷ = bo+ bix + b₂x₂ + bts, where x₁ is square footage, x2₂ is number of bedrooms, x3 is number of baths, and y is the response variable "asking price." (c) Test Ho: B₁ B₂ B3 = 0 versus H₁: at least one of the B, 0 at the a= 0.05 level of significance. (d) Test the hypotheses Ho: B₁-0 versus H₁: B₁ 0, Ho: B₂0 versus H₁: B₂ 0, and Ho: B3 - 0 versus H₁: B30 at the a= 0.05 level of significance. (e) Remove the explanatory variable with the highest P-value and compute the least-squares regression equation. Are all the slope coefficients significantly different from zero? If not, remove the explanatory variable with the higher P-value and compute the least-squares regression equation. (1) Draw residual plots, a boxplot of the residuals, and a normal probability plot of the residuals to assess the adequacy of the model found in part (e). (g) Interpret the regression coefficients for the least-squares regression equation found in part (e). 3