E(y) = β0 + β1x1 + β2x2 + β3x3

where y represents exam score (0 to 100 points), x 1 represents the amount paid to a teacher (in dollars), x 2 represents the number of hours of sleep per week, and x3 represents number of study hours.
Suppose that we used a sample of 100 students to fit the following prediction equation:

ŷ= 65 + 1.5x1 + 0.2x2 + 0.5x3

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.

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.

Step-by-step 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!

75

step-by-step explanation: