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

Question

3 years ago

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

e.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.

Mathematics

2 answers:

Tju [1.3M] · Answer 1 · 2022-01-19T00:26:58+03:00

Answer:

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

Step-by-step 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,

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