Under the assumptions of the Simple Linear Regression (SLR) model:a. Show that Cov(Bo, B₁) = = [Hint: write Cov(ŝo, ß₁) = Cov(Ỹ – Î₁T, Î₁).]Sxx-b. Use the answer from part (a) to show that Bo and B₁ are independent ifx=0. [Hint: if W and X are linear combinations of independentnormal random variables, then Cov(W, X) = 0 W and X independent.]

Using the simple linear regression model We have to show that Cov(β0^,β1^)=-x¯/(σ2/Sxx)And based on…

Answered: Under the assumptions of the Simple…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In the linear regression equation ŷ = bo + b1x, the notation bị is called O independent variable O y-intercept dependent variable O slope O none of the above
n0 puimz. Find the regression model. Y 12 - 9. 7 4 4 11 O A) y=5,27-0,11x O B) y=5,27+0,11x O C) y=2,56+5,43x O D) y=-0,11+5,27x O E) y=-3,21+2,11x
In a comprehensive road test on new car models, one variable measured is the time it takes a car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: y = Elapsed time (in seconds) from 0 mph to 60 mph MAX: x = Maximum speed attained (miles per hour) The simple linear model E(y) = Bo + B1x was fit to the data. Computer printouts for the analysis are given below: NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60 PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T CONSTANT 187171 0.63708 29.38 0.0000 0.0000 MAX -0.08365 0.00491 -17.05 0.6960 0.6937 R-SQUARED RESID. MEAN SQUARE (MSE) 1.28695 ADJUSTED R-SQUARED STAND ARD DEVIATION 113444 SOURCE DF MS F REGRESSION 374.285 0.0000 374.285 1.28695 290.83 RESIDUAL 127 163.443 TOTAL 128 537.728 CASES INCLUDED 129 MISSING CASES 0 Fill in the blank: "At a =.05, there is between maximum speed and acceleration time." O sufficient evidence of a…
An investigator has reported the data tabulated below. It is known that such data can be modeled by the following equation: x = e(v-b)/a where a and b are parameters. Use a transformationto linearize this equation and then employ linear regression to determine a and b. 1 2 3 4 5 y 0.5 2 2.9 3.5 4
What kind of variable is x in terms of linear regression? * a) Independent b) Dependent c) Both of the above d) None of the above
4. Consider the Normal regression problem: Y,- N(a + Br, o) where a, 3. are unknown. Recall the following: a = Y- 37 S = SY = En - F)(Y - Y). Show that S,y E,(r, - 2)Y- Show that Cov(Y, Y) = for all i. Use part a and b and linearity of Covariance to show that Cov(8, Y) = 0. Show that Var(3) = ) „how that Cov(a, B) = - (Hint: part a , b and d may be useful in this cauculation).
Consider the regression model Y₁ = BX; +u; Y Where ui and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ = Show that ẞ is a linear function of Y₁, Y2,..., Yn. Show that ẞ is conditionally unbiased. 1. E (YiX1, X2,..., Xn) = == X + +Yn) 2. E(B|×1, X2,..., Xn) = E = B Χ | (X1, X2,..., Xn) = where Y and X are the sample means of Y; and X;, respectively.
Given are five observations for two variables, x and y. xi 3 12 6 20 14 yi 55 45 50 15 20 #1) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. y= #2) Use the estimated regression equation to predict the value of y when x = 13.
A linear multiple regression model is given as: Y = βo + β1 X1 + β2 X2 + μ a. Determine the parameters of this model b. Explain the circumstance under which X1 be called an endogenous variable?
assume the final regression equation from the stepwise regression analysis of the dependent variable cost (C) and the 10 potential independent variables is as follows: C = -5000 + 75 D + 0.4 S - 130 PT + 100 NE Given that the final model is valid, interpret the coefficient of NE: On average, a plant constructed in northeast region of USA costs _____ than a plant constructed in other regions, while keeping other variables constant A) 100 dollars more B) 100 millions of dollars more C) 100 millions of dollars less D) 100 dollars less
3

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