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-hat = 50.57+0.4845x. Which of the following is the best description of the slope of the line? Group of answer choices As the Exam1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points. As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 50.57 points. As the Exam 3 score increases by 1 point, the student's Exam 1 score will increase, on average by 0.4845 points. 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:

A simple linear regression analysis was conducted to predict the Exam 3 score of students in STA 2023 based on their Exam 1 score.

Thus, Exam 3 score becomes the dependent variable and exam 1 score is the independent variable.

The regression equation is given by:

$\hat{y} = 50.57+0.4845x$

Comparing the equation to a linear equation:

$y = mx + c$

m = 0.4845

c = 50.57

Where m is the slope and tells the rate of change and c is the y intercept that is the value of y when x is 0.

When, there is a increase in x, we can write:

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

Thus, the slope of equation can be interpreted 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.