(c) Fill in the values for the following ANOVA table: Source of Variation Sum of Squares df Mean Square F Regression on Xi, X2 Error Total (Corrected) (d) State the nul and alternative hypotheses associated with the F test from the ANOVA table in part (c) and do the F test (e) Compute R2 (f) Construct a 95% prediction interval for a new response Yo when X1 = 1.5 and X2-1 are observed for explanatory variable. v (g) Is the linear relationship between the mean response and the value of Xi significant whern X2 is not included in the model? Test H0 : E(X)-A) against H. : E(X) ß0+AXil. (h) Is the coefficient for X1 significant after X2 has been included in the model? (i) What can your conclude about the importance of Xi and X2 in describing the mean response?
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0 2 10 0 2 8 Consider the multiple regression model where є¡ ~ iid Ņ(0, σ*) for i = i, 2, 3, 4, 5...
3. (20 pts) Do not use a computer to complete the answers for this problem. Show your work in all...
Please solve the problems (d),(e),(f),(g)
3. (20 pts) Do not use a computer to complete the answers for this problem. Show your work in all problems. Consider the following data: 2 -2 2 1 0 4 0 2 10 0 -2 8 Consider the multiple regression model where ci ~ iid N(0, σ*) for i 1, 2, 3, 4, 5. (a) Fill in the values for response vector, design matrix and coefficient vector: X- (b) Find the vector of least...
1. Consider the linear regression model iid 220 with є, 면 N(0, σ2), i = 1, . . . , n. Let Yh = β0+ßX, be the MLE of t...
1. Consider the linear regression model iid 220 with є, 면 N(0, σ2), i = 1, . . . , n. Let Yh = β0+ßX, be the MLE of the mean at covariate value Xh . (f) Suppose we estimate ơ2 by 82-SSE/(n-2). Derive the distribution for You can use the fact that SSE/σ2 ~ X2-2 without proof. (g) What is a (1-a)100% confidence interval for y? (h) Suppose we observe a new observation Ynet at covariate value X =...
3. Consider the multiple linear regression model iid where Xi, . . . ,Xp-1 ,i are observed covariate values for observation i, and Ei ~N(0,ơ2) (a) What is the interpretation of B1 in this model? (b)...
3. Consider the multiple linear regression model iid where Xi, . . . ,Xp-1 ,i are observed covariate values for observation i, and Ei ~N(0,ơ2) (a) What is the interpretation of B1 in this model? (b) Write the matrix form of the model. Label the response vector, design matrix, coefficient vector, and error vector, and specify the dimensions and elements for each. (c) Write the likelihood, log-likelihood, and in matrix form. aB (d) Solve : 0 for β, the MLE...
Consider the simple linear regression model: HARD1 = β0 + β1*SCORE + є, where є ~...
Consider the simple linear regression model: HARD1 = β0 + β1*SCORE + є, where є ~ N(0, σ). Note: HARD1 is the Rockwell hardness of 1% copper alloys and SCORE is the abrasion loss score. Assume all regression model assumptions hold. The following incomplete output was obtained from Excel. Consider also that the mean of x is 81.467 and SXX is 81.733. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.450969 Standard Error Observations 15 ANOVA df...
1. Consider the following linear regression model: (a) Which assumptions are needed to make the B,...
1. Consider the following linear regression model: (a) Which assumptions are needed to make the B, unbiased estimators for the B, (b) Explain how one can test the hypothesis that A +As = 0 by means of a t-test. (c) Explain how one can test the hypothesis that A-A-0. Indicate the relevant test statistic. (d) Suppose that ri is an irrelevant explanatory variable in the population model and that you estimate the model including both and r2. What are the...
Q4.. [40 points] Consider the multiple linear regression model given by y - XB -+ s,...
Q4.. [40 points] Consider the multiple linear regression model given by y - XB -+ s, where y and e are vectors of size 8 × 1, X ls a matrix of size 8 x 3 and Disa vector of sze 3 × 1. Also, the following information are available e = 22 y -2 and XTy 3 1. [10 points) Estimate the regression coefficients in the model given above? 2. [4 points] Estimate the variance of the error term...
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the var...
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: 0.04 + 0.28X1 + 0.84X2-0.06x3 + 0.14x4 y She would like to conduct significance tests for a multiple regression relationship. She uses the F test to determine whether a significant relationship exists...
e. Consider the multiple regression model Y = X1?1 + X2?2 + . The Gauss-Markov conditions...
e. Consider the multiple regression model Y = X1?1 + X2?2 + .
The Gauss-Markov conditions hold. Show that Y0 (I ? H)Y = Y0 (I ?
H1)Y ? ?ˆ0 2X0 2 (I ? H1)Y.
e. Consider the multiple regression model Ý = XiA + X2ß2 + E. The Gauss-Markov conditions hold. show that Y'(l-H)Y-Y'(1-HJY-? (1-H,)Y
Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2 ) observations, where σ 2 > 0 is unknown. Consider testing H0 : σ 2 = σ 2 0 versus H1 : σ 2 6= σ 2 0
Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2
) observations, where σ
2 > 0 is
unknown. Consider testing
H0 : σ
2 = σ
2
0 versus H1 : σ
2
6= σ
2
0
;
where σ
2
0
is known.
(a) Derive a size α likelihood ratio test of H0 versus H1. Your rejection region should
be written in terms of a sufficient statistic.
(b) When the null...
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the follow...
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...
Please solve the problems (d),(e),(f),(g)
3. (20 pts) Do not use a computer to complete the answers for this problem. Show your work in all problems. Consider the following data: 2 -2 2 1 0 4 0 2 10 0 -2 8 Consider the multiple regression model where ci ~ iid N(0, σ*) for i 1, 2, 3, 4, 5. (a) Fill in the values for response vector, design matrix and coefficient vector: X- (b) Find the vector of least...
1. Consider the linear regression model iid 220 with є, 면 N(0, σ2), i = 1, . . . , n. Let Yh = β0+ßX, be the MLE of the mean at covariate value Xh . (f) Suppose we estimate ơ2 by 82-SSE/(n-2). Derive the distribution for You can use the fact that SSE/σ2 ~ X2-2 without proof. (g) What is a (1-a)100% confidence interval for y? (h) Suppose we observe a new observation Ynet at covariate value X =...
3. Consider the multiple linear regression model iid where Xi, . . . ,Xp-1 ,i are observed covariate values for observation i, and Ei ~N(0,ơ2) (a) What is the interpretation of B1 in this model? (b) Write the matrix form of the model. Label the response vector, design matrix, coefficient vector, and error vector, and specify the dimensions and elements for each. (c) Write the likelihood, log-likelihood, and in matrix form. aB (d) Solve : 0 for β, the MLE...
1. Consider the following linear regression model: (a) Which assumptions are needed to make the B, unbiased estimators for the B, (b) Explain how one can test the hypothesis that A +As = 0 by means of a t-test. (c) Explain how one can test the hypothesis that A-A-0. Indicate the relevant test statistic. (d) Suppose that ri is an irrelevant explanatory variable in the population model and that you estimate the model including both and r2. What are the...
Q4.. [40 points] Consider the multiple linear regression model given by y - XB -+ s, where y and e are vectors of size 8 × 1, X ls a matrix of size 8 x 3 and Disa vector of sze 3 × 1. Also, the following information are available e = 22 y -2 and XTy 3 1. [10 points) Estimate the regression coefficients in the model given above? 2. [4 points] Estimate the variance of the error term...
4. Testing for significance Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x1, x2, X3, and x4: Using data with n = 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: 0.04 + 0.28X1 + 0.84X2-0.06x3 + 0.14x4 y She would like to conduct significance tests for a multiple regression relationship. She uses the F test to determine whether a significant relationship exists...
e. Consider the multiple regression model Y = X1?1 + X2?2 + .
The Gauss-Markov conditions hold. Show that Y0 (I ? H)Y = Y0 (I ?
H1)Y ? ?ˆ0 2X0 2 (I ? H1)Y.
e. Consider the multiple regression model Ý = XiA + X2ß2 + E. The Gauss-Markov conditions hold. show that Y'(l-H)Y-Y'(1-HJY-? (1-H,)Y
Consider a multiple regression model of the dependent variable y on independent variables x1, X2, X3, and x4: Using data with n 60 observations for each of the variables, a student obtains the following estimated regression equation for the model given: y0.35 0.58x1 + 0.45x2-0.25x3 - 0.10x4 He would like to conduct significance tests for a multiple regression relationship. He uses the F test to determine whether a significant relationship exists between the dependent variable and He uses the t...
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