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Answer: For an increase of GBP 1,000 in income, expected annual savings will increase by GBP 240.
## Explanation The regression equation is: **Annual Savings = 0.24 × Household Income − 25.66** Let's analyze each option: **Option A: Incorrect** - The intercept term (-25.66) represents the expected annual savings when household income is zero, not the average error term. - In regression analysis, the error term has an expected value of zero by assumption. **Option B: Incorrect** - When household income is zero, annual savings = 0.24 × 0 − 25.66 = -25.66 GBP - This means households with no income would have negative savings (i.e., they would be dissaving or borrowing). **Option C: Correct** - The coefficient of 0.24 means that for every 1 GBP increase in household income, annual savings increases by 0.24 GBP. - Therefore, for a 1,000 GBP increase in income: 0.24 × 1,000 = 240 GBP increase in savings. - This is the correct interpretation of the slope coefficient in a linear regression. **Option D: Incorrect** - For a decrease of 2,000 GBP in income: 0.24 × (-2,000) = -480 GBP - This means expected annual savings would DECREASE by 480 GBP, not increase. **Key Points:** - The slope coefficient (0.24) represents the marginal effect of income on savings - The intercept (-25.66) represents the baseline savings when income is zero - R² = 0.50 indicates that 50% of the variation in savings is explained by income
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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.