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Consider the simple linear model y = ẞ0 + ẞ1x + €. (a) (8 points) Show that the least squares estimates of the slope and intercept of a line may be expressed as: - Σ(xi — x) (yi — ÿ) i=1 n Σ(α; - π)2 i=1 and ẞo = ÿ – B₁x. (you can use the formulas derived in lecture notes). (b) (6 points) Show that if = 0, the estimated slope B₁ and intercept Bo are uncorrelated under the assumptions of the standard statistical model for simple linear regression, i.e. Cov(Bo, B1) = 0. (c) (6 points) Use part (a) to show that the line fit using the least squares method passes through the point (x, y).

Consider the simple linear model y = ẞ0 + ẞ1x + €. (a) (8 points) Show that the least squares estimates of the slope and intercept of a line may be expressed as: - Σ(xi — x) (yi — ÿ) i=1 n Σ(α; - π)2 i=1 and ẞo = ÿ – B₁x. (you can use the formulas derived in lecture notes). (b) (6 points) Show that if = 0, the estimated slope B₁ and intercept Bo are uncorrelated under the assumptions of the standard statistical model for simple linear regression, i.e. Cov(Bo, B1) = 0. (c) (6 points) Use part (a) to show that the line fit using the least squares method passes through the point (x, y).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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help me with abc please. please handwrite if possible. please don't use AI tools to answer

Consider the simple linear model y = ẞ0 + ẞ1x + €. (a) (8 points) Show that the least squares estimates of the slope and intercept of a line may be expressed as: - Σ(xi — x) (yi — ÿ) i=1 n Σ(α; - π)2 i=1 and ẞo = ÿ – B₁x. (you can use the formulas derived in lecture notes). (b) (6 points) Show that if = 0, the estimated slope B₁ and intercept Bo are uncorrelated under the assumptions of the standard statistical model for simple linear regression, i.e. Cov(Bo, B1) = 0. (c) (6 points) Use part (a) to show that the line fit using the least squares method passes through the point (x, y).
Transcribed Image Text:Consider the simple linear model y = ẞ0 + ẞ1x + €. (a) (8 points) Show that the least squares estimates of the slope and intercept of a line may be expressed as: - Σ(xi — x) (yi — ÿ) i=1 n Σ(α; - π)2 i=1 and ẞo = ÿ – B₁x. (you can use the formulas derived in lecture notes). (b) (6 points) Show that if = 0, the estimated slope B₁ and intercept Bo are uncorrelated under the assumptions of the standard statistical model for simple linear regression, i.e. Cov(Bo, B1) = 0. (c) (6 points) Use part (a) to show that the line fit using the least squares method passes through the point (x, y).
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