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.

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? 单项选择题

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