I'm having trouble in part B of this exercise!!!
Consider the regression line that passes through the
origin.
a)Prove that, in this case, the least squares estimators
for the slope is
b) Prove that
is an unskewed estimator of
.
I'm having trouble in part B of this exercise!!! Consider the regression line that passes through...
Exercise 2b please!
Exercise 1 Consider the regression model through the origin y.-β1zi-ci, where Ei ~ N(0,o). It is assumed that the regression line passes through the origin (0, 0) that for this model a: T N, is an unbiased estimator of o2. a. Show d. Show that (n-D2 ~X2-1, where se is the unbiased estimator of σ2 from question (a). Exercise2 Refer to exercise 1 a. Show that is BLUE (best linear unbiased estimator) b. Show that +1 has...
There are important applications in which due to known scientific constraints, the Problem 5 of 5 regression line must also go through origin (i.e. the intercept must be zero). In other words, the model should read Y Bai,i 1,2,.,n This model is often called the regression through the origin model. Assuming that e's are independent with distribution N(0, o2) (a) Show that the least squares estimator of the slope is ΣL Υ B = Σ (b) Show that B in...
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive the formula for the least squares estimator of p The least squares objective function is OA. n (v2-bo-bx?) i-1 Ов. O B. n (M-bo-bX) /# 1 n Click to select your answer and then click Check Answer. Exercise 4.11 OA n Σ (--B,χ?) O B. E (Y-bo-b,X)2 j= 1 n Σ (Υ-Βo-bΧ) 3. j= 1 D. n Σ (Υ-0-b,) i- 1 Click to select...
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
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...
1. Consider the simple linear regression model where Bo is known. a) Find the least squares estimator bi of B (b) Is this estimator unbiased? Prove your result. (c) Find an expression for Var(b1x1, ,xn) in terms of x1, ,xn and σ2.
(2 points) Find the least squares regression line ý = b + b through the points (-2,0), (2,9), (5,15), (7,20),(10,26). For what value of cis y = 0? =
6. Consider the following regression model without an intercept: Y = B,X, +U, One possible estimator for this model is given by: BE ANXJ Assume that you can make all of the usual ordinary least squares assumptions about the model, including the assumption that the true model does not include an intercept. Is B, an unbiased estimator? Please prove your conclusion, being sure to state the assumptions you use. [5 points]
down options for Part (h) are: (d) or (b)Complete parts (a) through (h) for the data below. x2030405060y7975706250 (b) Find the equation of the line containing the points (30,75) and (60,50). (c) Graph the line found in part (b) the scatter diagram. Choose the correct graph below. (d) By hand, determine the least-squares regression line. (e) Graph the least-squares regression line on the scatter diagram. (f) Compute the sum of the squared residuals for the line found in part (b) (g) Compute the sum of the squared...
(1 point) Find the least-squares regression line ý = b + b 2 through the points (-2,0), (1,7), (6, 15), (7, 20), (9, 24). For what value of I is ŷ = 0?