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.The range of exam scores for both tests was about 30 points to 102 points. Which of the following is the best description of the y-intercept of the line(if appropriate)?1. When the exam 1 grade increases by 1 point, the exam 3 grade increases by 0.4845. 2. When the exam 1 grade increases by 1 point, the exam 3 grade increases by 50.57. 3. The expected Exam 3 score for someone that made a 0 on Exam 1 is a 50.57. 4. Should not be interpreted.

Answer 1

The Answer is b

Explanation:

Answer 2

Option 3) The expected Exam 3 score for someone that made a 0 on Exam 1 is a 50.57.

Explanation:

We are given the following in the question:

`\hat{y}(x) = 50.57+0.4845x`

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

`\hat{y}`: The dependent variable, Exam 3 score

x: The independent variable, Exam 1 score

Comparing to general linear equation,

`y = mx + c`

We get,

m = 0.4845, c = 50.57

where

c is the y - intercept and the score in exam 3 when exam score is 0.

`\hat{y}(0) = 50.57+0.4845(0)\\\hat{y}(0) = 50.57`

m is the slope and tells us about the rate of change.

When exam 1 grade is increased by 1, 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(x+1-x)\\\hat{y}(x+1)-\hat{y}(x) = 0.4845`

Thus, the y-intercept for the given equation can be interpreted as

Option 3) The expected Exam 3 score for someone that made a 0 on Exam 1 is a 50.57.