b) If two regression models are fit to the same population having two different samples, what are the various criteria for deciding which model better fits the data than the other? Explain your answer with reasonable arguments. c) Test whether the model as a whole is significant or not, applying a systematic procedure, for the following model. y^ = -1.9451+0.1609 x2+0.2 x3 R? = 0.9510 n= 10 Critical value: 4.74
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- Consider the following ANOVA table for a multiple regression model relating housing prices (in thousands of dollars) to the number of bedrooms in the house and the size of the lot on which the house was built (in square feet). There were 77 total observations. Estimated Price = 27,756.55 + 2431.81 (Bedrooms) + 0.2732 (Lot Size) ANOVA df SS MS F Significance F Regression 2 357,061.4229 178,530.7115 21.0765 5.6943E-08 Residual 74 626,824.0170 Total 76 983,885.4399 8470.5948 Compute the adjusted coefficient of determination for this regression model. Round your answer to four decimal places.Define Interpretation of coefficients in polynomial regression models?Consider the following ANOVA table for a multiple regression model relating housing prices (in thousands of dollars) to the number of bedrooms in the house and the size of the lot on which the house was built (in square feet). There were 90 total observations. Estimated Price = 24,838.74 + 2339.88 (Bedrooms) + 0.2685 (Lot Size) ANOVA df SS MS F Regression 2 382,993.4921 Residual 87 627,839.9910 Significance F 191,496.7461 26.5358 1.0066E-09 7216.5516 Total 89 1,010,833.4831 Compute the adjusted coefficient of determination for this regression model. Round your answer to four decimal places.
- Consider the following ANOVA table for a multiple regression model relating housing prices (in thousands of dollars) to the number of bedrooms in the house and the size of the lot on which the house was built (in square feet). There were 90 total observations. Estimated Price = 24,838.74 + 2339.88 (Bedrooms) + 0.2685 (Lot Size) ANOVA df Regression 2 382,993.4921 Residual 87 627,839.9910 Total 89 1,010,833.4831 SS MS 191,496.7461 26.5358 7216.5516 F Significance F 1.0066E-09 What percent of variation in housing prices is explained by the number of bedrooms and lot size? Round your answer to two decimal places.Consider the regression model Y₁ = BX; +u; Where u; and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ß = Show that ẞ is a linear function of Y₁, Y2,..., Yn. where Y and X are the sample means of Y; and X;, respectively. Show that ẞ is conditionally unbiased. 1. E (Y;|X1, X2,..., Xn) = 1 -B (X ₁ + X 2 + ... + Xn) Х answer these part correctly + ... + Y) +X₂+ ... + Xn) = B 2. E (B|×₁, ×2,..., Xn) = E | (X1, X2,..., Xn) BX; ☑ BX BYa) The R? should not be used to choose the best econometric model specification in multiple regression models. True or False
- What are the measures of fit that are commonly used for multiple regressions? How can an adjusted R2 take on negative values?(2)What would the consequence be for a regression model if theerrors were not homoscedastic?All the regression assumptions lie on the residuals, for both simple and multiple regression. True or False?
- 2. Consider a two variable regression model, which satisfies all the Gauss Markov assumptions except that the error variance is proportional to X² i.e.E(u?) = o²X? Y₁ = B₁ + B₂X₁ + Ui How would you obtain the best linear unbiased estimates from the above regression.Consider the regression model Yi=bot Bi Xitui Suppose that you know Bo = 0. Derive the formula for the least squares estimator of B₁. The least squares objective function is O A. n O B. O C. O D. E (Yi-bo-b1Xi) i=1 n Σ (Yi-bo-biXi) i=1 2 n Σ (v₁²-bo-b₁x₁²) i=1 n E (Yi-bo-b+Xi) 3 i=1Problem 3 Consider the following multiple regression model Y = Bo + B₁X₁i + B2X2i + B3X3i + Ui You want to consider certain hypotheses involving more than one parameter, and you know that the regression error is homoskedastic. You decide to test the joint hypotheses using the homoskedasticity-only F-statistics. For each of the cases below specify a restricted model and indicate how you would compute the F-statistic to test for the validity of the restrictions at the 1% level. 1. B₁-B2; B3 = 0 = 2. B1 + 3₂+ B3 = 1 3. B1 B2; B3 0 =