(a) Do you think if it is suitable for the (ordinary) least square regression technique to apply the data (x4, Y;)? Give a brief reasoning
(b) Construct a transformed model so that you can use the ordinary least square method
(c) Find the parameter estimates for the transformed model in (b)
WIS (d) Find the weighted least squares estimator of BWLS and B
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4. (20 pts) Consider the following regression model, i = 1,2. ,...n, N (0, 2/i) where...
3. (20 pts) Suppose that we have 4 observations for 3 variables y,I, 2 and consider...
3. (20 pts) Suppose that we have 4 observations for 3 variables y,I, 2 and consider a problem of regressing y on two (qualitative) variables r, 2. Data: 22 obs no. y (Income) 2 (Management Status) I (Gender) 1 None Female 2 None Male Yes Female Yes Male 4 To handle the qualitative variables r, 12, we define dummy variables 1, 22 as for 1, 22= Yes Male for 1, 219 22 -1. for 22= None for 1= Female -1,...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
Consider the following simple regression model: where the e, are independent errors with E(ed-0 and var(et)-Ơ2X?...
Consider the following simple regression model: where the e, are independent errors with E(ed-0 and var(et)-Ơ2X? a. In this case, would an ordinary least squares regression provide you with the best b. c. linear unbiased estimates? Why or why not? What is the transformed model that would give you constant error variance? Given the following data: y = (4,3,1,0,2) and x = (1,2,1,3,4) Find the generalized least squares estimates of β1 and β2 (Do this by hand! Not with excel)
3. Consider a forecasting model with a trend where t is the t index for t...
3. Consider a forecasting model with a trend where t is the t index for t 1,2, . .T. The ordinary least squares estimator of Bo and Bi are given as 81 ewhere (b) Suppose that the unit of ye is in billions but you mistakenly used w-t/1000, which is in trillions, and estimate a model Find the ordinary least squares estimator for O and δι in terms of A and β1
012. (a) The ordinary least squares estimate of B in the classical linear regression model Yi...
012. (a) The ordinary least squares estimate of B in the classical linear regression model Yi = α + AXi + Ui ; i=1,2, , n and xi = Xi-K, X-n2Xī i- 1 Show that if Var(B-.--u , no other linear unbiased estimator of β n im1 can be constructed with a smaller variance. (All symbols have their usual meaning) 18
Q. 1 Consider the multiple linear regression model Y = x3 + €, where e indep...
Q. 1 Consider the multiple linear regression model Y = x3 + €, where e indep MV N(0,0²V) and V +In is a diagonal matrix. a) Derive the weighted least squares estimator for B, i.e., Owls. b) Show Bwis is an unbiased estimator for B. c) Derive the variances of w ls and the OLS estimator of 8. Is the OLS estimator of still the BLUE? In one sentence, explain why or why not.
Problem 7. Consider the simple linear regression model Y1 = Bo + BiX; +€; for i=1,2,...,n...
Problem 7. Consider the simple linear regression model Y1 = Bo + BiX; +€; for i=1,2,...,n where the errors Eį are uncorrelated, have mean zero and common variance Varſei] = 02. Suppose that the Xį are in centimeters and we want to write the model in inches. If one centimeter = c inch with c known, we can write the above model as Yį = y +71 Zitki where Zi is Xi converted to inches. Can you obtain the least-squared...
please don't copy, thx Question 2. Consider the model Yij = uị + Rij, Rij~N(0,02), i...
please don't copy, thx
Question 2. Consider the model Yij = uị + Rij, Rij~N(0,02), i = 1,2; j = 1,2, ..., Ni. Part A. Determine using least squares the parameter estimates. Part B. State the estimate of variance in the model. Part C. Clearly show that that ūı = 71+ is an unbiased estimator of Mz. Part D. The average grade of 32 Nano Engineering students in STAT 353 is 75% with a standard deviation of 5%. The average...
4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose...
4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose the following sample is observed. 6 X 2 10 8 4 Y 3 4 5 6 2 4.8 3.Y 4c (1) Find the OLS estimates for B, and B2. (2) Compute the estimate of Var(u). (3) What are the variances of the OLS estimates? (4) Compute the coefficient of determination. (5) Show the relationship between r2 and Dxy (6) Compute the correlation coefficient pxy...
Consider the simple linear regression model where Bo is known. (a) Find the least squares estimator...
Consider the simple linear regression model where Bo is known. (a) Find the least squares estimator bi of β1- (b) Is this estimator unbiased? Prove your result
3. (20 pts) Suppose that we have 4 observations for 3 variables y,I, 2 and consider a problem of regressing y on two (qualitative) variables r, 2. Data: 22 obs no. y (Income) 2 (Management Status) I (Gender) 1 None Female 2 None Male Yes Female Yes Male 4 To handle the qualitative variables r, 12, we define dummy variables 1, 22 as for 1, 22= Yes Male for 1, 219 22 -1. for 22= None for 1= Female -1,...
2. Consider the simple linear regression model: where e1, .. . , es, are i.i.d. N (0, o2), for i= 1,2,... , n. Suppose that we would like to estimate the mean response at x = x*, that is we want to estimate lyx=* = Bo + B1 x*. The least squares estimator for /uyx* is = bo bi x*, where bo, b1 are the least squares estimators for Bo, Bi. ayx= (a) Show that the least squares estimator for...
Consider the following simple regression model: where the e, are independent errors with E(ed-0 and var(et)-Ơ2X? a. In this case, would an ordinary least squares regression provide you with the best b. c. linear unbiased estimates? Why or why not? What is the transformed model that would give you constant error variance? Given the following data: y = (4,3,1,0,2) and x = (1,2,1,3,4) Find the generalized least squares estimates of β1 and β2 (Do this by hand! Not with excel)
3. Consider a forecasting model with a trend where t is the t index for t 1,2, . .T. The ordinary least squares estimator of Bo and Bi are given as 81 ewhere (b) Suppose that the unit of ye is in billions but you mistakenly used w-t/1000, which is in trillions, and estimate a model Find the ordinary least squares estimator for O and δι in terms of A and β1
012. (a) The ordinary least squares estimate of B in the classical linear regression model Yi = α + AXi + Ui ; i=1,2, , n and xi = Xi-K, X-n2Xī i- 1 Show that if Var(B-.--u , no other linear unbiased estimator of β n im1 can be constructed with a smaller variance. (All symbols have their usual meaning) 18
Q. 1 Consider the multiple linear regression model Y = x3 + €, where e indep MV N(0,0²V) and V +In is a diagonal matrix. a) Derive the weighted least squares estimator for B, i.e., Owls. b) Show Bwis is an unbiased estimator for B. c) Derive the variances of w ls and the OLS estimator of 8. Is the OLS estimator of still the BLUE? In one sentence, explain why or why not.
Problem 7. Consider the simple linear regression model Y1 = Bo + BiX; +€; for i=1,2,...,n where the errors Eį are uncorrelated, have mean zero and common variance Varſei] = 02. Suppose that the Xį are in centimeters and we want to write the model in inches. If one centimeter = c inch with c known, we can write the above model as Yį = y +71 Zitki where Zi is Xi converted to inches. Can you obtain the least-squared...
please don't copy, thx
Question 2. Consider the model Yij = uị + Rij, Rij~N(0,02), i = 1,2; j = 1,2, ..., Ni. Part A. Determine using least squares the parameter estimates. Part B. State the estimate of variance in the model. Part C. Clearly show that that ūı = 71+ is an unbiased estimator of Mz. Part D. The average grade of 32 Nano Engineering students in STAT 353 is 75% with a standard deviation of 5%. The average...
4. (60%) Consider the following linear regression model s XIXJ YB1+B2X u, i 1,2.. .n Suppose the following sample is observed. 6 X 2 10 8 4 Y 3 4 5 6 2 4.8 3.Y 4c (1) Find the OLS estimates for B, and B2. (2) Compute the estimate of Var(u). (3) What are the variances of the OLS estimates? (4) Compute the coefficient of determination. (5) Show the relationship between r2 and Dxy (6) Compute the correlation coefficient pxy...
Consider the simple linear regression model where Bo is known. (a) Find the least squares estimator bi of β1- (b) Is this estimator unbiased? Prove your result
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