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Consider a population regression equation: Y =B₁ + B₁X + U₁ where and are the intercept and slope parameters, respectively. Assume that E(u) = 0. Note that the equation does not take into account yet the changes in the measurement of X. e. Show that Cov(X,Y) Var(X) B₁ Given the measurement change in X, how will the following parameters change? f. Slope parameter, B₁ g. Intercept parameter, B

Consider a population regression equation: Y =B₁ + B₁X + U₁ where and are the intercept and slope parameters, respectively. Assume that E(u) = 0. Note that the equation does not take into account yet the changes in the measurement of X. e. Show that Cov(X,Y) Var(X) B₁ Given the measurement change in X, how will the following parameters change? f. Slope parameter, B₁ g. Intercept parameter, B

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 6PPS
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Consider a population regression equation: Y = B₁ + B₁₂X + U₁ where B and B are the intercept and slope parameters, respectively. Assume that E(u) = 0. Note that the equation does not take into account yet the changes in the measurement of X. e. Show that Cov(X,Y) 1 Var (X) B₁ Given the measurement change in X, how will the following parameters change? f. Slope parameter, B₁ g. Intercept parameter, B 2 Consider a random sample of (X, Y), with a sample size of n. How will the following estimators change given the measurement change in X? h. Sample mean, x i. Sample variance,
Transcribed Image Text:Consider a population regression equation: Y = B₁ + B₁₂X + U₁ where B and B are the intercept and slope parameters, respectively. Assume that E(u) = 0. Note that the equation does not take into account yet the changes in the measurement of X. e. Show that Cov(X,Y) 1 Var (X) B₁ Given the measurement change in X, how will the following parameters change? f. Slope parameter, B₁ g. Intercept parameter, B 2 Consider a random sample of (X, Y), with a sample size of n. How will the following estimators change given the measurement change in X? h. Sample mean, x i. Sample variance,
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