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

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 - 5X  i

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

First, restating the given information: the regression equation is Ŷi = 2 - 5Xi, where Y is Daily Gas Costs (in dollars) and X is Temperature (in °C). The coefficient on Temperature is -5, which represents the marginal effect of a one-unit change in Temperature on the predicted Daily Gas Costs.

Now, evaluate the impact of increasing Temperature by 1°C. In a linear regression model, a change of ΔX = +1 leads to a predicted change in Ŷ equal to the coefficient times ΔX: ΔŶ = -5 × (+1) = -5.

Interpretation of this result: with Temperature rising by 1°C, the model predicts Daily Gas Costs would decrease by $5, due to the negative relationship between Temperature and gas costs captured by the coefficient -5.

Since there is only one answer option provided, we focus on that statement: 'For an increase in Temperature by 1°C, we would expect a $5 decrease in Daily Gas Costs.' This aligns with the coefficient -5 and the sign convention in the equation.

A few additional clarifications to avoid common pitfalls: the intercept (2) is the predicted Y when X = 0 and does not inform the change in Y due to a change in X; the slope (-5) governs the rate of change of Y with respect to X; and the unit of the predicted change is dollars, matching the Y variable.

If Temperature were to decrease by 1°C (ΔX = -1), the predicted change would be ΔŶ = -5 × (-1) = +$5, i.e., an increase of $5 in Daily Gas Costs, illustrating how the sign of the coefficient dictates the direction of change with respect to X.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 3A 简单线性回归小测：第 3A 部分

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