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7.22. In the regression model Y; = Bo + B1Xi + B2(3X} – 2) +Ei, i...
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...
Type or pas 2. Let the population regression model between a dependent variable y and an...
Type or pas
2. Let the population regression model between a dependent variable y and an independent variable is given by y= Bo+ B1 x x+ u Suppose that E(u|x) = E(u) = 0 and V(ux) = o2. Based on a random sample ((y, ) i = 1,2,...n) of size n such that (xi- )2>0, let Bo and B be the OLS estimates of Bo and Bi respectively. Answer the following questions (c) Let B i Show that if B1...
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...
ek-tin Based on the following regression output, what proportion the total variation in Y is explained...
ek-tin
Based on the following regression output, what proportion the total variation in Y is explained by X? Regression Statistics Multiple R 0.917214 R Square 0.841282 Adjusted R Square 0.821442 Standard Error 9.385572 Observations 10 ANOVA di SS MS Significance F 1 Regression 3735.3060 3735.30600 42.40379 0.000186 Residual 8 704.7117 88.08896 9 Total 4440.0170 Coefficients Standard Error t Stat P-value Lower 95% Intercept 31.623780 10.442970 3.028236 0.016353 7.542233 X Variable 1.131661 0.173786 6.511819 0.000186 0.730910 o a. 0.917214 o b.9.385572...
are the assumptions behind any multiple regression model? (b). For a multiple regression model Y-Bo + βιΧ. + β2X2 +β3Xs + € where is the error term, to represent the relationship between Y and th...
are the assumptions behind any multiple regression model? (b). For a multiple regression model Y-Bo + βιΧ. + β2X2 +β3Xs + € where is the error term, to represent the relationship between Y and the four X- variables. We got the following results from the data: Source Sum of Squares degrees of freedom mean squares Regression 1009.92 Residual Total 2204.94 34 And also you are given: Variable X1 Σ.tx-xr 123.74 72.98 12.207 -Pr values -11.02 5.13 X2 X3 Y-intercept is...
Consider the regression equation Y = Bo+B1Xi+u; where E[u;|Xi]=0 for all i = 1, ..., n....
Consider the regression equation Y = Bo+B1Xi+u; where E[u;|Xi]=0 for all i = 1, ..., n. Let B 1 be the OLS estimator for B 1. Which statement is the most irrelevant to the consistency of B1? Hint: see Lecture Note 2 (p.25-p.28) a. When n is large, the estimator B 1 is near the population parameter B1 O". Consistency of B1 is mathematically written as B1-B1 VB) is inversely proportional to the sample size n. Od. RMSE is close...
3. (20 pts) Suppose that we have 4 observations for 3 variables y , x\, X2...
3. (20 pts) Suppose that we have 4 observations for 3 variables y , x\, X2 and consider a problem of regressing y on two (qualitative) variables x\, xz. Data y (Income) x (Gender) X2 (Management Status) obs no. Female None 2 Male None 3 Female Yes 4 Male Yes Y4 To handle the qualitative variables x\, x2, we define dummy variables z1, 22 as Male for for 1, 1, T2= Yes Z1= Z2= -1 for for 1 1 =...
2. For the quadratic model, where Y = Bo + B1 X1 + B2 X1 2...
2. For the quadratic model, where Y = Bo + B1 X1 + B2 X1 2 + ε, set forth the formula used to calculate the elasticity of Y with respect to X1.
1. A professor examined the relationship between the number of hours devoted to reading, each week...
1. A professor examined the relationship between the number of hours devoted to reading, each week Y and the independent variable social class X1), the number of years of school completed x2 and reading speed X3, in pages read per hour. The following ANOVA table obtained from a stepwise regression procedure for a sample of 19 women over 60. A) Fill in the missing values. DESS Source Regression x3 MS P value 1 1058.628 Residual 585.02 Regression X2 X3 183.743...
Thank you for your answer = = Exercise 2.4. Define the functions f(Bo, B1, B2) 21–1(Y;...
Thank you for your answer
= = Exercise 2.4. Define the functions f(Bo, B1, B2) 21–1(Y; – Bo – B1Xi – B2X?)2 and g(B0, B1) 2_1(Y; – Bo – B1X;)?, and let (Bo, ß1, B2) be the minimiser of f($0, B1, B2) and (Bo, Bi) the minimiser of g(Bo, B1). Explain, or prove, that 05 f(Bo, ß1, B2) <g(Bo, Bi).
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...
Type or pas
2. Let the population regression model between a dependent variable y and an independent variable is given by y= Bo+ B1 x x+ u Suppose that E(u|x) = E(u) = 0 and V(ux) = o2. Based on a random sample ((y, ) i = 1,2,...n) of size n such that (xi- )2>0, let Bo and B be the OLS estimates of Bo and Bi respectively. Answer the following questions (c) Let B i Show that if B1...
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...
ek-tin
Based on the following regression output, what proportion the total variation in Y is explained by X? Regression Statistics Multiple R 0.917214 R Square 0.841282 Adjusted R Square 0.821442 Standard Error 9.385572 Observations 10 ANOVA di SS MS Significance F 1 Regression 3735.3060 3735.30600 42.40379 0.000186 Residual 8 704.7117 88.08896 9 Total 4440.0170 Coefficients Standard Error t Stat P-value Lower 95% Intercept 31.623780 10.442970 3.028236 0.016353 7.542233 X Variable 1.131661 0.173786 6.511819 0.000186 0.730910 o a. 0.917214 o b.9.385572...
are the assumptions behind any multiple regression model? (b). For a multiple regression model Y-Bo + βιΧ. + β2X2 +β3Xs + € where is the error term, to represent the relationship between Y and the four X- variables. We got the following results from the data: Source Sum of Squares degrees of freedom mean squares Regression 1009.92 Residual Total 2204.94 34 And also you are given: Variable X1 Σ.tx-xr 123.74 72.98 12.207 -Pr values -11.02 5.13 X2 X3 Y-intercept is...
Consider the regression equation Y = Bo+B1Xi+u; where E[u;|Xi]=0 for all i = 1, ..., n. Let B 1 be the OLS estimator for B 1. Which statement is the most irrelevant to the consistency of B1? Hint: see Lecture Note 2 (p.25-p.28) a. When n is large, the estimator B 1 is near the population parameter B1 O". Consistency of B1 is mathematically written as B1-B1 VB) is inversely proportional to the sample size n. Od. RMSE is close...
3. (20 pts) Suppose that we have 4 observations for 3 variables y , x\, X2 and consider a problem of regressing y on two (qualitative) variables x\, xz. Data y (Income) x (Gender) X2 (Management Status) obs no. Female None 2 Male None 3 Female Yes 4 Male Yes Y4 To handle the qualitative variables x\, x2, we define dummy variables z1, 22 as Male for for 1, 1, T2= Yes Z1= Z2= -1 for for 1 1 =...
2. For the quadratic model, where Y = Bo + B1 X1 + B2 X1 2 + ε, set forth the formula used to calculate the elasticity of Y with respect to X1.
1. A professor examined the relationship between the number of hours devoted to reading, each week Y and the independent variable social class X1), the number of years of school completed x2 and reading speed X3, in pages read per hour. The following ANOVA table obtained from a stepwise regression procedure for a sample of 19 women over 60. A) Fill in the missing values. DESS Source Regression x3 MS P value 1 1058.628 Residual 585.02 Regression X2 X3 183.743...
Thank you for your answer
= = Exercise 2.4. Define the functions f(Bo, B1, B2) 21–1(Y; – Bo – B1Xi – B2X?)2 and g(B0, B1) 2_1(Y; – Bo – B1X;)?, and let (Bo, ß1, B2) be the minimiser of f($0, B1, B2) and (Bo, Bi) the minimiser of g(Bo, B1). Explain, or prove, that 05 f(Bo, ß1, B2) <g(Bo, Bi).
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