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2024 PEA Q16

For a given data set, let the least squares regression line be y=10+2xy=10+2x. It is given that variance of xx is 99 and variance of yy is 8181. What is the correlation coefficient between xx and yy?

Reveal answer and solution

Answer

C

Solution

  1. 1

    The slope of the OLS regression of yy on xx satisfies β^=r⋅σyσx\hat\beta = r\cdot\dfrac{\sigma_y}{\sigma_x}. Hence

  2. 2
    2=r⋅819=r⋅93=3r ⟹ r=23. 2 = r\cdot\frac{\sqrt{81}}{\sqrt{9}}=r\cdot\frac{9}{3}=3r\ \Longrightarrow\ r=\frac{2}{3}.
  3. 3

    (Since β^>0\hat\beta>0, rr is also positive.)

Answer structure / marking notes

Use σy/σx\sigma_y/\sigma_x, not the variance ratio.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2024/ISI_MSQE_PEA_2024_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.