Lets say we're predicting marathon runners time in hours by their age in decades. We end up getting a positive and significant coefficient of 0.1 and a intercept of 3. If we used age in years instead of age in decades, what will happen?

Question

BlackTom AI · Accepted Answer

We start by understanding how changing the unit of age affects the regression terms. The original model is predicting marathon time as a function of age in decades: y = intercept + 0.1 * (age in decades). Since age in decades = age in years ÷ 10, we can rewrite the model as y = intercept + 0.1 * (age_years / 10) = intercept + 0.01 * age_years.

Option 1 says: 'The coefficient on age will get 10 times smaller, the coefficient on the intercept will stay the same.' This aligns with the algebra above: the age coefficient becomes 0.01 when using years, which is indeed 10 times smaller than 0.1, and the intercept remains unchanged at 3.

Option 2 states: 'The coefficient on age will get 10 times smaller, the coefficient on the intercept will get 10 times smaller.' The first part is correct about the coefficient, but the intercept should not change with the unit transformation—it should stay at 3 in this setup—so this is incorrect.

Option 3 asserts: 'The coefficient on age will get 10 times larger, the coefficient on the intercept will stay the same.' Increasing the coefficient by a factor of 10 contradicts the derived 0.01 from 0.1 when converting decades to years, making this option false.

Option 4 claims: 'The coefficient on age will get 10 times larger, the coefficient on the intercept will stay the same.' While the intercept staying the same is fine, the age coefficient being larger is not consistent with the relationship age_years = 10 * age_decades; the correct scaling reduces the coefficient, not enlarges it.

In summary, only the first option correctly describes the effect of switching from age in decades to age in years on both the slope and the intercept in this linear model.

Lets say we're predicting marathon runners time in hours by their age in decades. We end up getting a positive and significant coefficient of 0.1 and a intercept of 3. If we used age in years instead of age in decades, what will happen?单项选择题

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