Calculating the equation of a regression line
8:11
Calculating the equation of a regression line
Jul 12, 2017
Khan Academy
SOLVED: Consider the standard bivariate regression model y = β0 β1x u where the standard assumptions hold. Prove the following: 1 (a) R^2 = ˆβ1^2 σˆ^2x σˆ^2y. You can proceed with the following steps:i. Take the formula for R^2 = SSE/SST, and write the summations that the numerator and denominator represent. ii. Use the fact that ˆyi = ˆβ0 ˆβ1xi and ¯y = ˆβ0 ˆβ1x¯ in the numerator. iii. Use the fact that Σ(xi−x¯)^2 Σ(yi−y¯)^2 = 1/(n−1) Σ(xi−x¯)^2 1/(n−1
SOLVED: Consider the standard bivariate regression model y = β0 ΅
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