2. (8 points) Let be the slope estimate from a simple regression of y on...

Transcribed Image Text:

2. (8 points) Let ß₁ be the slope estimate from a simple regression of y on x, and assume that there is variation in the sample values of both y and x. 2.1. Derive an expression for R² in terms of the slope estimate, ₁; the sample variance of x, Var(x); and the sample variance of y, Var(y). Hint: Express R² as a ratio of two variances, then use the formula for the estimated regression line. If ß₁ = 0, must it be that R² = 0? 2.2. If R² = 0, must it be that ₁ = 0? 2. (8 points) Let ß₁ be the slope estimate from a simple regression of y on x, and assume that there is variation in the sample values of both y and x. 2.1. Derive an expression for R² in terms of the slope estimate, ₁; the sample variance of x, Var(x); and the sample variance of y, Var(y). Hint: Express R² as a ratio of two variances, then use the formula for the estimated regression line. If ß₁ = 0, must it be that R² = 0? 2.2. If R² = 0, must it be that ₁ = 0?

Answer rating: 100% (QA)

21 To derive the expression for R in terms of the slope estimate the sample variance of x Varx and the sample variance of y Vary we start by expressin... View the full answer