1) Given the model y = βο + β1X1 + β2X2 + β3X3 + ε if...
1) Given the model y = βο + β1X1 + β2X2 + β3X3 + ε if we plot y against X1 and get a parabola shaped curve then what does this suggest? Choose the correct answer.
a) E(ε) does not equal zero
b) an X12 term is needed
c) an X22 term is needed
d) constant variance violated
Homework Answers
Given the model y = βο + β1X1 + β2X2 + β3X3 + ε if we plot y against X1 and get a parabola shaped curve then what does this suggest?
Answer - an X12 term is needed
Exhibit a. y = β0 + β1x1 + β2x2 + ε b. E(y) = β0 +...
Exhibit a. y = β0 + β1x1 + β2x2 + ε b. E(y) = β0 + β1x1 c. = b0 + b1 x1 + b2 x2 d. E(y) = β0 + β1x1 + β2x2 3. Refer to Exhibit. Which equation describes the multiple regression equation? a. equation a b. equation b c. equation c d. equation d
When estimating y = β0 + β1x1 + β2x2 + β3x3 + ε, you wish to...
When estimating y = β0 + β1x1 + β2x2 + β3x3 + ε, you wish to test H0: β1 = β2 = 0 versus HA: At least one βi ≠ 0. The value of the test statistic is F(2,20) = 2.50 and its associated p-value is 0.1073. At the 5% significance level, the conclusion is to ________. Multiple Choice a. reject the null hypothesis; we can conclude that x1 and x2 are jointly significant b. not reject the null hypothesis;...
1.The following tables give the results for the full model, as well as a reduced model, containing only experience Test Ho: ß,-Bs-0 vs HA: β2 and/or β3 # 0 Complete Model: Y-βο + β1X1 + β2X2 + β3Xs +...
1.The following tables give the results for the full model, as well as a reduced model, containing only experience Test Ho: ß,-Bs-0 vs HA: β2 and/or β3 # 0 Complete Model: Y-βο + β1X1 + β2X2 + β3Xs + ε ANOVA MS P-value df 76.9 Regression Residual Total 2470.4 823.5 224.7 2695.1 .0000 10.7 21 24 Reduced Model: Y = β0 + β X + ε MS df 1 23 24 value 2394.9 2394.9 183.5 0.0000 300.2 13.1 2695.1 Regression...
31. Suppose you fit a multiple linear regression model y = β0 + β1x1 + β2x2...
31. Suppose you fit a multiple linear regression model y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε to n = 30 data points and obtain SSE = 282 and R^2 = 0.8266 a.) Find an estimate of s^2 for the multiple regression model (a) s^2 ≈ 30.9856 (b) s^2 ≈ 28.6021 (c) s^2 ≈ 1.3111 (d) s^2 ≈ 29.7938 (d) b.) Based on the data information given in a.), you use F-test to test H0...
Consider the regression model y=β0+β1x1+β2x2+u Suppose this is estimated by Feasible Weighted Least Squares (FWLS) assuming...
Consider the regression model y=β0+β1x1+β2x2+u Suppose this is estimated by Feasible Weighted Least Squares (FWLS) assuming a conditional variance function Varux=σ2h(x). Which of the following statements is correct? A) The function h(x) does not need to be estimated as part of the procedure B) If the assumption about the conditional variance of the error term is incorrect, then FWLS is still consistent. C) FWLS is the best linear unbiased estimator when there is heteroscedasticity. D) None of the above answers...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β ̂_3 are 1.86 and .29, respectively. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α...
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and...
1. Consider the following simple regression model: y = β0 + β1x1 + u (1) and the following multiple regression model: y = β0 + β1x1 + β2x2 + u (2), where x1 is the variable of primary interest to explain y. Which of the following statements is correct? a. When drawing ceteris paribus conclusions about how x1 affects y, with model (1), we must assume that x2, and all other factors contained in u, are uncorrelated with x1. b....
1.Given the Multiple Linear regression model as Y-Po + β.X1 + β2X2 + β3Xs + which in matrix notation is written asy-xß +ε where -έ has a N(0,a21) distribution + + ßpXo +ε A. Show that the OLS estimat...
1.Given the Multiple Linear regression model as Y-Po + β.X1 + β2X2 + β3Xs + which in matrix notation is written asy-xß +ε where -έ has a N(0,a21) distribution + + ßpXo +ε A. Show that the OLS estimator of the parameter vector B is given by B. Show that the OLS in A above is an unbiased estimator of β Hint: E(β)-β C. Show that the variance of the estimator is Var(B)-o(Xx)-1 D. What is the distribution o the...
Using the appropriate model, sample size n, and output below: Model: y = β0 + β1x1...
Using the appropriate model, sample size n, and output below: Model: y = β0 + β1x1 + β2x2 + β3x3 + ε Sample size: n = 16 Regression Statistics Multiple R 0.9975 R Square 0.9950 Adjusted R Square 0.9937 Standard Error 440.3187 Observations 16 ANOVA DF SS MS F Significance F Regression 3 461,801,144.1072 153,933,714.7024 793.9616 0.0000 Residual 12 2,326,566.6701 193,880.5558 Total 15 464,127,710.7773 (1) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round...
Question 2 1 pts suppose you estimate the following model: Y-α + β1 X1 + β2X2...
Question 2 1 pts suppose you estimate the following model: Y-α + β1 X1 + β2X2 + γΖ + u You wish to test the null hypothesis: Ho; A-:-As against a two-sided alternative. You do so, and get the following estimates: βι 5.23, B2--4.56, 8e (A) 2.09, 8e (%) 1.47, 8e (A-A) 2.24, 8e (A +%)-0.94 What is the value of the relevant test statistic for this hypothesis test? 4.37 0.71 0.30 10.41
1.The following tables give the results for the full model, as well as a reduced model, containing only experience Test Ho: ß,-Bs-0 vs HA: β2 and/or β3 # 0 Complete Model: Y-βο + β1X1 + β2X2 + β3Xs + ε ANOVA MS P-value df 76.9 Regression Residual Total 2470.4 823.5 224.7 2695.1 .0000 10.7 21 24 Reduced Model: Y = β0 + β X + ε MS df 1 23 24 value 2394.9 2394.9 183.5 0.0000 300.2 13.1 2695.1 Regression...
1.Given the Multiple Linear regression model as Y-Po + β.X1 + β2X2 + β3Xs + which in matrix notation is written asy-xß +ε where -έ has a N(0,a21) distribution + + ßpXo +ε A. Show that the OLS estimator of the parameter vector B is given by B. Show that the OLS in A above is an unbiased estimator of β Hint: E(β)-β C. Show that the variance of the estimator is Var(B)-o(Xx)-1 D. What is the distribution o the...
Question 2 1 pts suppose you estimate the following model: Y-α + β1 X1 + β2X2 + γΖ + u You wish to test the null hypothesis: Ho; A-:-As against a two-sided alternative. You do so, and get the following estimates: βι 5.23, B2--4.56, 8e (A) 2.09, 8e (%) 1.47, 8e (A-A) 2.24, 8e (A +%)-0.94 What is the value of the relevant test statistic for this hypothesis test? 4.37 0.71 0.30 10.41
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