Consider the following model:

E(y) = βo + β1x1 + β2x2 + β3x3 + β4x1x2

where y represents exam score (0 to 100 points), x1 represents the amount paid to a tutor (in dollars) in the week before the exam, x2 represents the number of hours of sleep in the week before the exam, and as represents number of study hours in the week before the exam. How many independent variables are included in this model?

a. 3
b. 2
c. 1
d. 4

a. 3

Step-by-step explanation:

An independent variable is the variable that is changed in an experiment to test its effects on the dependent variable. i.e. inputs

A dependent variable is the variable being tested, measured or predicted in an experiment. I.e a outcome

In this case, the the effects of the amount tutors are paid a week before exam, the amount of sleep before exam and the number of study hours are input variables to determine or predict a students score in exam

The independent variables are;

x1 =represents the amount paid to a tutor (in dollars) in the week before the exam

x2 = represents the number of hours of sleep in the week before the exam

x3 = number of study hours in the week before the exam

The dependent variable is the exam score

B0, B1, B2,B3, B4 are coefficients

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)