Question

A simple linear regression analysis was conducted to predict the Exam 3 score of students in STA 2023 based on their Exam 1 score. The analysis yielded the following results:
y-^ = 50.57+0.4845x.
1. Which of the following is the best description of the slope of the line?
Group of answer choices:
O As the Exam1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points.
O As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 50.57 points.
O As the Exam 3 score increases by 1 point, the student's Exam 1 score will increase, on average by 0.4845 points.
O As the Exam 3 score increases by 1 point, the student's Exam 1 score will increase, on average by 50.57 points.

Answer 1

Answer:

Option A)  As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points.

Step-by-step explanation:

We are given the following in the equation:

$y(x) = 50.57+0.4845x$

where, above equation is a  linear regression equation to predict the Exam 3 score of students in STA 2023 based on their Exam 1 score.

Here,

y is the dependent variable that is score of exam 3.

x is the independent variable that is the score of exam 1.

Comparing the given equation to a linear equation, we have,

$y = mx + c$

Slope, m = 0.4845

Intercept, c = 50.57

We define the slope as rate of change.

If there is a increase in x by 1 unit, then,

$y(x) = 50.57+0.4845x\\y(x+1) = 50.57+0.4845(x+1)\\y(x+1)-y(x) = 50.57+0.4845(x+1)-50.57-0.4845x\\y(x+1)-y(x) = 0.4845(x+1-x)\\y(x+1)-y(x) = 0.4845$

Thus, we can interpret the slope of the line as

Option A) As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points.