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Answer: For an increase of GBP 1,000 in income, expected annual savings will increase by GBP 240.
## Explanation **Regression Equation:** Annual Savings = 0.24 × Household Income − 25.66 **Interpreting the coefficients:** - Slope coefficient (0.24): For every GBP 1 increase in household income, annual savings increases by GBP 0.24 - Intercept (-25.66): When household income is 0, annual savings would be -GBP 25.66 (theoretical) **Analyzing each option:** **Option C (Correct):** - For GBP 1,000 increase in income: 0.24 × 1,000 = GBP 240 increase in savings - This correctly interprets the slope coefficient **Option A (Incorrect):** - The intercept (-25.66) is not the average error term - The error term in regression has mean zero by construction **Option B (Incorrect):** - With zero income: 0.24 × 0 − 25.66 = -GBP 25.66, not GBP 0 **Option D (Incorrect):** - For GBP 2,000 decrease in income: 0.24 × (-2,000) = -GBP 480 (decrease, not increase) - The interpretation of direction is wrong **Additional context:** - R² = 0.50 means 50% of the variability in savings is explained by income - All coefficients being statistically significant means these relationships are reliable in the population
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Using data from a pool of mortgage borrowers, a credit risk analyst performed an ordinary least squares regression of annual savings (in GBP) against annual household income (in GBP) and obtained the following relationship: Annual Savings = 0.24 × Household Income − 25.66, R² = 0.50
Assuming that all coefficients are statistically significant, which interpretation of this result is correct?
A
For this sample data, the average error term is GBP -25.66.
B
For a household with no income, annual savings is GBP 0.
C
For an increase of GBP 1,000 in income, expected annual savings will increase by GBP 240.
D
For a decrease of GBP 2,000 in income, expected annual savings will increase by GBP 480.
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