A car manufacturer wants to predict the mileage (y) of their cars based on the engine size (x) in litres.

The regression model output is:

lm(formula = y ~ x)

Coefficients:
(Intercept) x
30.0 -5.0

Which of the following statements is true?

Question

A car manufacturer wants to predict the mileage (y) of their cars based on the engine size (x) in litres.

The regression model output is:

lm(formula = y ~ x)

Coefficients:
(Intercept)       x
     30.0       -5.0

Which of the following statements is true?

BlackTom AI · Accepted Answer

We start by restating the scenario and what the regression output tells us. The model y ~ x has an intercept of 30.0 and a slope for x of -5.0. This means two things: at x = 0, the predicted mileage is 30 units (whatever the unit is), and for every 1 unit increase in engine size x (in litres), the predicted mileage y decreases by 5 units.

Now, evaluate the implications step by step:
- The negative slope (-5.0) indicates an inverse relationship between engine size and mileage: as engine size increases, mileage tends to decrease.
- Intercept interpretation: when x is 0 (an impractical but mathematically defined point), y would be 30. This does not override the key pattern captured by the slope; it just anchors the regression line.
- The core practical takeaway is about the association: larger engines are associated with lower mileage, because the slope is negative.

Given these readings, any candidate statement should reflect that larger engine size corresponds to reduced mileage. If a statement says that mileage is lower when engine size is larger, it aligns with the negative slope interpretation. Conversely, statements implying no relationship, a positive relationship, or that increased engine size increases mileage would contradict the slope estimate.

In this specific question, the only provided option (lower mileage is associated with larger engine size) directly expresses the negative association implied by the slope. The logic hinges on the fundamental meaning of a negative regression coefficient for x in a simple linear model: as x grows, y shrinks on average.

If you consider potential edge cases, remember that the interpretation assumes the model is specified correctly, the relationship is approximately linear within the data range, and that units are consistent. But within the given output, the slope of -5.0 is the driving indicator of a negative association between engine size and mileage.

A car manufacturer wants to predict the mileage (y) of their cars based on the engine size (x) in litres. The regression model output is: lm(formula = y ~ x) Coefficients: (Intercept) x 30.0 -5.0 Which of the following statements is true?单项选择题

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