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