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Exercise 9.5 Take the linear model Yi = x'iiß1 + x2iß2 + éj E (Xili) =...
Exercise 9.8 You want to test Ho: B2 = 0 against Hı: B2 + 0 in...
Exercise 9.8 You want to test Ho: B2 = 0 against Hı: B2 + 0 in the model Yi = x1ib1 + x2iß2 + li E (Xili) = 0 You read a paper which estimates model yi =x7+ (x2i-xi) Ya+ and reports a test of Ho :Y2 = 0 against Hı:Y2+0. Is this related to the test you wanted to conduct?
Exercise 5 Consider a linear model with n = 2m in which Yi = Bo +...
Exercise 5 Consider a linear model with n = 2m in which Yi = Bo + Bici + Eigi = 1,..., m, and Yi = Bo + B2X1 + Ei, i = m + 1, ...,n. Here €1,..., En are i.i.d. from N(0,0), B = (Bo, B1, B2)' and o2 are unknown parameters, X1, ..., Xn are known constants with X1 + ... + Xm = Xm+1 + ... + Xn = 0. 1. Write the model in vector form...
A regression model that is linear in the unknown parameters is a linear regression model. A)...
A regression model that is linear in the unknown parameters is a linear regression model. A) True B) False The test for significance of regression in multiple regression involves testing the hypotheses Ho: B1=B2=B3=0 versus H1: B1≠B2≠B3≠0. A) True B) False The ANOVA is used to test for significance of regression in multiple regression. A) True B) False
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
Let Yi,... , Yv be independent random variables with E(Yi) A,ơ for 1,..., N. Is this a generalized linear model? Give r...
Let Yi,... , Yv be independent random variables with E(Yi) A,ơ for 1,..., N. Is this a generalized linear model? Give reasons for all 2 s this a generalized linear modelr Give reasons for your answer.
Let Yi,... , Yv be independent random variables with E(Yi) A,ơ for 1,..., N. Is this a generalized linear model? Give reasons for all 2 s this a generalized linear modelr Give reasons for your answer.
1. What is the coefficient of determination and why is it important? What does it show...
1. What is the coefficient of determination and why is it important? What does it show us? 2. What is heteroskedasticity, which assumption of the linear model does it violate, and how can we test for it? 3. What is multicollinearity? What problems can it cause to our results? 4. If you decide to scale both your dependent and your independent variable by 100, how will your regression results change? 5. Using N=40 observations, you estimate the following model y...
Exercise 9.19 An economist estimates Yi = xlißi + x2iß2 + ei by least-squares and tests...
Exercise 9.19 An economist estimates Yi = xlißi + x2iß2 + ei by least-squares and tests the hypothesis Ho: B2 = 0 against Hı: B2 #0. She obtains a Wald statistic Wn = 0.34. The sample size is n= 500. (a) What is the correct degrees of freedom for the x2 distribution to evaluate the significance of the Wald statistic? (b) The Wald statistic Wn is very small. Indeed, is it less than the 1% quantile of the appropriate x2...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
4) Consider n data points with 2 covariates and observation {xi,i, Vi,2, yi); i -1,... ,n,...
4) Consider n data points with 2 covariates and observation {xi,i, Vi,2, yi); i -1,... ,n, where yi 's are indicator variable for the experiment that is if a particular medicine is effective on some individual. Here, xi1 and ri.2 are age and blood pressure of i th individual, respectively. Our assumption is that the log odds ratio follows a linear model. That is p-P(i-1) and 10i b) What should be a good estimator for ?,A, e) Suppose. On, A,n...
Exercise 9.8 You want to test Ho: B2 = 0 against Hı: B2 + 0 in the model Yi = x1ib1 + x2iß2 + li E (Xili) = 0 You read a paper which estimates model yi =x7+ (x2i-xi) Ya+ and reports a test of Ho :Y2 = 0 against Hı:Y2+0. Is this related to the test you wanted to conduct?
Exercise 5 Consider a linear model with n = 2m in which Yi = Bo + Bici + Eigi = 1,..., m, and Yi = Bo + B2X1 + Ei, i = m + 1, ...,n. Here €1,..., En are i.i.d. from N(0,0), B = (Bo, B1, B2)' and o2 are unknown parameters, X1, ..., Xn are known constants with X1 + ... + Xm = Xm+1 + ... + Xn = 0. 1. Write the model in vector form...
A simple linear regression model is given as follows Yi = Bo + B1Xi+ €i, for i = 1, ...,n, where are i.i.d. following N (0, o2) distribution. It is known that x4 n, and x = 0, otherwise. Denote by n2 = n - ni, Ji = 1 yi, and j2 = 1 1. for i = 1, ... ,n1 < n2 Lizn1+1 Yi. n1 Zi=1 1. Find the least squares estimators of Bo and 31, in terms of...
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
Let Yi,... , Yv be independent random variables with E(Yi) A,ơ for 1,..., N. Is this a generalized linear model? Give reasons for all 2 s this a generalized linear modelr Give reasons for your answer.
Let Yi,... , Yv be independent random variables with E(Yi) A,ơ for 1,..., N. Is this a generalized linear model? Give reasons for all 2 s this a generalized linear modelr Give reasons for your answer.
1. What is the coefficient of determination and why is it important? What does it show us? 2. What is heteroskedasticity, which assumption of the linear model does it violate, and how can we test for it? 3. What is multicollinearity? What problems can it cause to our results? 4. If you decide to scale both your dependent and your independent variable by 100, how will your regression results change? 5. Using N=40 observations, you estimate the following model y...
Exercise 9.19 An economist estimates Yi = xlißi + x2iß2 + ei by least-squares and tests the hypothesis Ho: B2 = 0 against Hı: B2 #0. She obtains a Wald statistic Wn = 0.34. The sample size is n= 500. (a) What is the correct degrees of freedom for the x2 distribution to evaluate the significance of the Wald statistic? (b) The Wald statistic Wn is very small. Indeed, is it less than the 1% quantile of the appropriate x2...
2.4 We have defined the simple linear regression model to be y =B1 + B2x+e. Suppose however that we knew, for a fact, that ßı = 0. (a) What does the linear regression model look like, algebraically, if ßı = 0? (b) What does the linear regression model look like, graphically, if ßı = 0? (c) If Bi=0 the least squares "sum of squares" function becomes S(R2) = Gyi - B2x;)?. Using the data, x 1 2 3 4 5...
4) Consider n data points with 2 covariates and observation {xi,i, Vi,2, yi); i -1,... ,n, where yi 's are indicator variable for the experiment that is if a particular medicine is effective on some individual. Here, xi1 and ri.2 are age and blood pressure of i th individual, respectively. Our assumption is that the log odds ratio follows a linear model. That is p-P(i-1) and 10i b) What should be a good estimator for ?,A, e) Suppose. On, A,n...
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