Weight (in kg) can be predicted from height (in cm) from the regression line: weight = −96 + 0.95 × height This regression line predicts that, on average, weight:

Question

BlackTom AI · Accepted Answer

Consider what the regression equation weight = −96 + 0.95 × height means for a one-centimetre increase in height.
Option a: 'increases by 0.95 kg for each 1 centimetre increase in height' is correct because the coefficient of height in the regression line is 0.95. This coefficient represents the expected change in weight for each additional centimetre in height, holding other factors constant.
Option b: 'increases by 96 kg for each 1 centimetre increase in height' misreads the intercept and the slope. The number 96 is the magnitude of the intercept (−96), not the per-centimetre change, and a positive 96 per cm would imply an enormous and unrealistic gain in weight with height, which the model does not indicate.
Option c: 'decreases by 96 kg for each 1 centimetre increase in height' also confuses the slope with the intercept magnitude and assigns an incorrect direction and unit. The slope is not −96, and even if the intercept were negative, it would not describe the per-centimetre change.
Option d: 'decreases by 0.95 kg for each 1 centimetre increase in height' reverses the sign of the slope. The coefficient 0.95 is positive, meaning weight increases with height, not decreases.
Overall, the key takeaway is that in a linear regression equation of the form weight = a + b × height, the slope b indicates the change in weight per unit rise in height. Here b = 0.95, so weight rises by 0.95 kg per additional centimetre of height, on average.

Weight (in kg) can be predicted from height (in cm) from the regression line: weight = −96 + 0.95 × height This regression line predicts that, on average, weight:单项选择题

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