Given a simple linear regression model, y=+B+, which following expressions are OLS estimators for ?iΣ(x₂-x);i=1Σ(x,-1) ²i=1iΟ Σ-16-06-5)Σ(x,-x) ²i=1xy2²Xi=1

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Answered: Given a simple linear regression model,…

A First Course in Probability (10th Edition)

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Consider the OLS regression equation: ŷ = 0 + Â₁×1 + B₂X2 + Â33. If the R² is close to zero, it implies O x3 is not highly correlated with X₁ O B3 is likely to be biased O B3 is likely to be unbiased O that we expect the estimate of B3 to be noisy.
Suppose we have a regression situation involving 3 predictor variables and an intercept, with the following model: Y = Bo + B1X1 + B2X2 + B3X3 + € where n = 15. We find the following regression output (with some values deleted). Coefficients: Estimate Std. Error (Intercept) 0.08544 0.11529 х1 x2 0.67800 1.06700 -0.85400 1.19700 x3 0.08700 2.86110 Suppose we wish to calculate a 95% confidence interval for B3 (the slope of x3), in the usual way. What is the upper bound of the interval?
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y 6. For this problem, use a linear regression model. 1 2 12 a) Use the correlation formula to the right to calculate the correlation R - 1 Sx Sy 11 п-1 n 8 14 SSR = 1 SST SSE 11 17 Coefficient of Deternination → R2 SST 14 16 b) Find R^2 using SSR/SST SST = v- 7)² Sum of Squares Total → 17 20 19 24 Sum of Squares Regression → SSR = 20 22 SSE = >v-y)? Sum of Squares Error → 25 27 c) Find the slope using the formula to the right -- Σ-3-) Slope a= d) Verify your answers to parts a,b,c using another method of your choice intercept b= y-ax where overbar denotes average e). Find the residual for x = 14 f) Use your regression equation to find the probable x-value for y = 83, you may round your answer to 2 decimal places. %3D
6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by OLS. (a) Show thatE ûi 0, where the û;'s are the regression residuals. i3D1 (b) Suppose we regress X; on û; by OLS, including a constant term in the regression. Show that the estimated coefficient on û; is equal to zero. (c) Suppose we regress Y; on the predicted value Y; by OLS, including a constant term in the regression. Show that the estimated coefficient on Y; is equal to one. (Hint: the regression residual is defined by û; = Y; – Y; where the predicted value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)

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Given a simple linear regression model, y=+B+, which following expressions are OLS estimators for ? i Σ(x₂-x)y; i=1 Σ(x,-1) ² i=1 i Ο Σ-16-06-5) Σ₁(x, -x) ² i=1 xy 2² X i=1