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

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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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