You have the following unstandardised regression model equation for a sample of data: Ŷi = 2 - 5Xi

Variable Y is “Daily Gas Costs” (in $)

Variable X is “Temperature” (in °C)

If Temperature was to increase by 1°C, what could we say about Daily Gas Costs?

Question

You have the following unstandardised regression model equation for a sample of data: Ŷi = 2 - 5Xi

Variable Y is “Daily Gas Costs” (in $)

Variable X is “Temperature” (in °C)

If Temperature was to increase by 1°C, what could we say about Daily Gas Costs?

BlackTom AI · Accepted Answer

Question restatement: You have the unstandardised regression model Ŷi = 2 - 5Xi, where Y is Daily Gas Costs in dollars and X is Temperature in °C. If Temperature increases by 1°C, what happens to Daily Gas Costs?

Option 1: 'For an increase in Temperature by 1°C, we would expect a $5 increase in Daily Gas Costs.' This option misreads the coefficient sign. The slope is negative (-5), which implies costs move in the opposite direction to temperature; a positive change in X should reduce Y, not increase it. The statement makes the relationship positive, which contradicts the model.

Option 2: 'For an increase in Temperature by 1°C, we would expect a $5 decrease in Daily Gas Costs.' Here the magnitude 5 matches the coefficient magnitude, but with the opposite sign. Since the coefficient of X is -5, a 1°C increase in temperature reduces the predicted Y by 5 dollars. This aligns with the regression equation and the interpretation of a negative slope.

Option 3: 'For an increase in Temperature by 1°C, we would expect a $1 increase in Daily Gas Costs.' This option assigns a change of $1 per 1°C, which is inconsistent with the given slope of -5. It confuses the marginal effect (slope) with a much smaller value and also ignores the negative sign.

Option 4: 'For an increase in Temperature by 1°C, we would expect a $1 decrease in Daily Gas Costs.' This option correctly notes a decrease but assigns the wrong magnitude, $1 instead of the correct $5, and thus does not reflect the slope magnitude of -5.

In summary, the regression equation Ŷi = 2 - 5Xi indicates that for every 1-unit increase in X (temperature), the predicted Y (daily gas costs) changes by -5 dollars. The intercept 2 is the predicted cost when temperature is zero, but does not affect the question about the change due to temperature. Therefore, the option stating a $5 decrease for a 1°C increase in temperature accurately embodies the slope and direction implied by the model, while the other options either flip the direction, misstate the magnitude, or both.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 3A

You have the following unstandardised regression model equation for a sample of data: Ŷi = 2 - 5Xi Variable Y is “Daily Gas Costs” (in $) Variable X is “Temperature” (in °C) If Temperature was to increase by 1°C, what could we say about Daily Gas Costs?

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