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](https://tex.z-dn.net/?f=%5Chat%7By%7D%20%3D%2050.57%2B0.4845x)
Comparing the equation to a linear equation:
![y = mx + c](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20c)
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](https://tex.z-dn.net/?f=%5Chat%7By%7D%28x%29%20%3D%2050.57%2B0.4845x%5C%5C%5Chat%7By%7D%28x%2B1%29%20%3D%2050.57%2B0.4845%28x%2B1%29%5C%5C%5Chat%7By%7D%28x%2B1%29%20-%20%5Chat%7By%7D%28x%29%20%3D%2050.57%2B0.4845%28x%2B1%29-%2850.57%2B0.4845x%29%5C%5C%5Chat%7By%7D%28x%2B1%29%20-%20%5Chat%7By%7D%28x%29%20%3D%200.4845)
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.