PEA 2025 PEA Q14 | ISI MSQE

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2025 PEA Q14

Two samples; $R^2$ of first $>$ $R^2$ of second. Which follows?

Reveal answer and solution

Answer

Solution

1
For a simple regression,
2
$R^2 = \hat\beta_1^2 \cdot \frac{S_{xx}}{S_{yy}}.$
3
A larger $R^2$ can result from a larger $|\hat\beta_1|$ , a larger $S_{xx}$ , or a smaller $S_{yy}$ . None of (A), (B), or (C) follows without further restrictions.

Answer structure / marking notes

A high $R^2$ does not imply a large slope; the variance of $X$ also matters.

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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.