Question

E ( y ) = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3

where LaTeX: yy represents exam score (0 to 100 points), LaTeX: x_1x 1 represents the amount paid to a teacher (in dollars), LaTeX: x_2x 2 represents the number of hours of sleep per week, and LaTeX: x_3x 3 represents number of study hours.

Suppose that we used a sample of 100 students to fit the following prediction equation:

y_hatLaTeX: \:=\:65\:+1.5x_1\:+\:0.2x_2\:+\:0.5x_3= 65 + 1.5 x 1 + 0.2 x 2 + 0.5 x 3

Choose the most accurate interpretation for the slope of the amount paid to a teacher (in dollars).

Group of answer choices

a.For each additional 1.5 dollars paid to a tutor, we expect exam score to increase by 1 point, holding number of hours of sleep per week and number of study hours fixed.

b.For each additional dollar paid to a tutor, we expect exam score to increase by 1.5 points, holding number of hours of sleep per week and number of study hours fixed.

c.For each additional dollar paid to a tutor, we expect exam score to increase by 1.5 points.

d.When the amount paid to a tutor, number of hours of sleep per week, and number of study hours are set to 0, we expect an exam score of 65 points.

Answer 1

b.For each additional dollar paid to a tutor, we expect exam score to increase by 1.5 points, holding number of hours of sleep per week and number of study hours fixed.

Explanation:

Hello!

For any multiple regression model, you can define the estimated slope as "the change or modification of the estimated average of Y when one of the explanatory variables increases one unit while the others remain constant.

In this example the dependant variable is:

Y: Exam score

And you have three explanatory variables:

X₁: salary of the teacher ($).

X₂: hours of sleep per week of a student.

X₃: number of study hours of a student.

The estimated model is ŷ= 65 + 1.5X₁ + 0.2X₂ + 0.5X₃

You need to interpret the estimated slope of the amount paid to the teacher b₁= 1.5

The units of the slope are units of Y by units of X, in this case, Y has no units so it is 1/$.

Then we can say that for every additional dollar paid to the teacher, the estimated mean score of the exam will increase by 1.5 1/$ while the weekly sleep hours and study hours remain constant.

I hope it helps!