X1 X2 Y X1 1.000 0.454 0.585 X2 0.454 1.000 0.342 Y 0.585 0.342 1.000 n=29...

Question

Question

n=29

Calculated the adjusted R²

math Statistics-And-Probability

Answer 1

Answer #1

r_x1 = correlation between Y and X1 = 0.59

r_x2 = correlation between Y and X2 = 0.34

r₁₂ = correlation between X2 and X1 = 0.45

R² is given by, R² = ( r_x1² + r_x2² - 2r_x1r_x2r₁₂ ) / ( 1 - r₁₂² )

= (0.59² + 0.34² - 2 *0.59*0.34*0.45) / ( 1 - 0.45² )

= 0.2775/ 0.7938 = 0.35

n = no of observations = 29

k = no of independents used = 2

Adjusted R² = 1 - (1 - R² )*[(n-1)/(n-(k+1))]

= 1 - (1 - 0.35)*[(29-1)/(29-(2+1))]

= 1 - (1 - 0.35)*[28/26]

= 1 - 0.7 = 0.3

Answer 2

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