3. Consider the simple linear regression model: y = Bo+ Br2 +ế, where the intercept term 3o is known. We assume that the errors have mean zero and unknown va Further, the errors are assumed to be uncorrelated and independent of the predictor. We have n data points: (yi, xi) for i = 1,2, ...,n, and use the least-squares method to estimate f data. (a) Here, Bo is not a parameter to be estimated, as we know its value; for example, Bo is 5 or 2 other value. Consequently, the least-squares criterion is a function of 3₁. Write down the lea criterion, S(B₁). (b) Find a single least-squares normal equation. (c) Show that the solution to the normal equation is n Yi Xi βο Σ!,α;

3. Consider the simple linear regression model: y = Bo+ Br2 +ế, where the intercept term 3o is known. We assume that the errors have mean zero and unknown va Further, the errors are assumed to be uncorrelated and independent of the predictor. We have n data points: (yi, xi) for i = 1,2, ...,n, and use the least-squares method to estimate f data. (a) Here, Bo is not a parameter to be estimated, as we know its value; for example, Bo is 5 or 2 other value. Consequently, the least-squares criterion is a function of 3₁. Write down the lea criterion, S(B₁). (b) Find a single least-squares normal equation. (c) Show that the solution to the normal equation is n Yi Xi βο Σ!,α;

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.4: Linear Regression

Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

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Please answer questions

3. Consider the simple linear regression model:
y = Bo + Bi +,
where the intercept term Bo is known. We assume that the errors have mean zero and unknown variance o².
Further, the errors are assumed to be uncorrelated and independent of the predictor.
We have n data points: (yi, xi) for i = 1, 2, ..., n, and use the least-squares method to estimate 3₁ with the
data.
(a) Here, Bo is not a parameter to be estimated, as we know its value; for example, Bo is 5 or 20 or some
other value. Consequently, the least-squares criterion is a function of 3₁. Write down the least-squares
criterion, S(3₁).
(b) Find a single least-squares normal equation.
(c) Show that the solution to the normal equation is
3₁
=
Ei=1 Yixi - Boi=1 ºi
Σ²=1x²
(d) Show that the expected value of 3₁ is E(3₁) = ß₁.
02
Σ₁x²*
(e) Show that the variance of B₁ is Var (3₁)
=

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