Answer-first summary for fast verification
Answer: 0.0956
The standard error of the slope coefficient β̂ is calculated using the formula: $$SEE_{\beta} = \sqrt{\frac{s^2}{n \times \hat{\sigma}_x^2}}$$ Where: - $s^2 = 20.45$ (estimated variance of the residuals) - $\hat{\sigma}_x^2 = 18.65$ (estimated variance of the independent variable) - $n = 10 \text{ years} \times 12 \text{ months/year} = 120$ (total number of observations) Plugging in the values: $$SEE_{\beta} = \sqrt{\frac{20.45}{120 \times 18.65}} = \sqrt{\frac{20.45}{2238}} = \sqrt{0.009138} = 0.0956$$ The intercept (β̂₀ = 0.65) and mean of x (μ̂ₓ = 0.61) are not needed for this calculation. The correct answer is 0.0956.
Author: Nikitesh Somanthe
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A regression analysis of monthly returns of a sales company on the market return over ten years gives an intercept of β̂₀ = 0.65, the slope β̂ = 1.65. Other quantities include: s² = 20.45, σ̂ₓ² = 18.65 and μ̂ₓ = 0.61. What is the standard error estimate of β̂?
A
0.0678
B
0.0845
C
0.0953
D
0.0956
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