Mathematics · Linear Models
Let p > 1 and 1 > ρ ≥ 0. Consider a multiple linear regression problem with p independent variables X 1 , X 2 , ..., X p and a dependent variable Y. Suppose that the correlation between Y and X i is ρ and the correlation between X i and X j is also ρ for all 1 ≤ i < j ≤ p. Which of the following statements is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The multiple correlation between Y and (X 1 , ..., X p ) is larger than or equal to ρ✓
- 2The multiple correlation between Y and (X 1 , ..., X p ) will be ρ only if ρ > 0
- 3The multiple correlation between Y and (X 1 , ..., X p ) tends to 1 as p → ∞
- 4The multiple correlation between Y and (X 1 , ..., X p ) is strictly less than ρ for all ρ
Correct answer
The multiple correlation between Y and (X 1 , ..., X p ) is larger than or equal to ρ
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