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2025 PEA Q15

sd(x)=2\mathrm{sd}(x) = 2, sd(y)=4\mathrm{sd}(y) = 4. The OLS slope of YY on XX equals:

Reveal answer and solution

Answer

B

Solution

  1. 1
    β^1=r⋅sysx=r⋅42=2r. \hat\beta_1 = r \cdot \frac{s_y}{s_x} = r \cdot \frac{4}{2} = 2r.

Answer structure / marking notes

The formula β^1=r⋅sy/sx\hat\beta_1 = r \cdot s_y/s_x is one of the most useful identities in simple regression.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2025/ISI_MSQE_PEA_2025_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.