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2025 PEA Q11

β^0=5\hat\beta_0 = 5, yˉ=65\bar y = 65, xˉ=90\bar x = 90. Predict yy for x=75x = 75.

Reveal answer and solution

Answer

A

Solution

  1. 1

    OLS line passes through (xˉ,yˉ)(\bar x, \bar y):

  2. 2
    yˉ=β^0+β^1xˉ  ⟹  65=5+90β^1  ⟹  β^1=6090=23. \bar y = \hat\beta_0 + \hat\beta_1 \bar x \;\Longrightarrow\; 65 = 5 + 90\hat\beta_1 \;\Longrightarrow\; \hat\beta_1 = \tfrac{60}{90} = \tfrac{2}{3}.
  3. 3

    Then

  4. 4
    y^(75)=5+23(75)=5+50=55. \hat y(75) = 5 + \tfrac{2}{3}(75) = 5 + 50 = 55.

Answer structure / marking notes

Use the fact that an OLS line with intercept passes through the sample means.

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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.