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.

Answer 2

The best fit line that gives the possible relation between the two Exam

scores variables is given by the regression line equation.

The correct option that is the best description of the slope of the line is the option;

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

Reasoning for the above selection

The linear regression analysis result is; $\hat{y}$ = 50.57 + 0.4845·x

From the above regression line equation, we have;

The regression analysis equation is a straight line equation, of the format;

y = m·x + c

Where;

m = The slope = The rate of change of y per unit change in x = 0.4845

c = The y-intercept = The initial value of y

Comparison with the straight line equation gives;

y = $\hat y$ = The Exam 3 score

x = Exam 1 score

The coefficient of x is the rate of change or the slope of Exam 3 score

following an increase in Exam 1 score by 1 point.

Therefore;

• The correct option is; As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points

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