Question

You want to know what will happen to the number of days people worked in the previous 12 months if they exercised more. You use a survey that includes data on both

(a) the average number of days people exercise for 30 minutes or more in a week (values: 1 through 7) and

(b) their days worked.

You run the following regression:

DaysWorked_i = α_0 + α_1WeeklyExercise_i + e_i

You obtain a coefficient estimate (α_1) of 0.06, with a p-value of 0.023.

What is the meaning of the regression coefficient?

Group of answer choices

Each additional day of exercise increases the number of days worked by 6, on average

Each additional day of exercise increases the number of days worked by 6 percentage points, on average

Each 1% increase in the number of days exercised increases the number of days worked by 6 percentage points, on average

Each 1% increase in the number of days exercised increases the number of days worked by 6

Answer 1

The regression coefficient of 0.06 with a p-value of 0.023 indicates the following choice:

Each additional day of exercise increases the number of days worked by 6 percentage points, on average

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This is the second choice in the group of options.

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Days of exercise are entered in the equation as average number of days, no further transformation is used.

The number of days worked is also entered as days.

Percentages are not used in the equation.

Thus the interpretation is straightforward - as the value of the independent variable (average days of exercise) increases, the value of the dependent variable also increases (on an average).

The slope of this relationship, dy/dx, tells us how many units of y change when one unit of x changes.

Here, 0.06 units of y change. This translates to a 6% change.