Question

a regression line for predicting students test scores from hours studied is given by y=5x+60, where x is the number of hours studied. what does the slope of the line represent?
○ for each additional point scored, the predicted hours studied increases by 5 hours.
○ for each additional hour studied, the predicted test score increases by 5 points.
○ for each additional hour studied, the predicted test score increases by 60 points.
○ for each additional test score, the predicted hours studied increases by 5 points.

question 8
5 pts
given the regression equation y=-2x+80, what does the y-intercept (80) represent in the context of predicting exam scores from absences?
a student with 80 absences is predicted to score 0 on the exam.
a student with zero absences is predicted to score 80 on the exam.
a student with zero absences is predicted to score -2 on the exam.
for each absence, the exam score decreases by 80 points.

Explanation:

First Question (Regression Line Slope Interpretation)

The regression line is \( y = 5x + 60 \), where \( x \) is hours studied and \( y \) is test score. The slope of a linear equation \( y = mx + b \) represents the change in \( y \) for a 1 - unit change in \( x \). Here, \( m = 5 \), so for each additional hour (\( x \)) studied, the predicted test score (\( y \)) increases by 5 points. Let's analyze the options:

• Option 1: Incorrect. The slope relates hours studied to test scores, not the other way around.
• Option 2: Correct. Matches the interpretation of the slope (change in \( y \) per change in \( x \)).
• Option 3: Incorrect. The y - intercept is 60, not related to the slope's interpretation.
• Option 4: Incorrect. The slope is about hours studied affecting test scores, not the reverse.

The regression equation is \( y=-2x + 80 \), where \( x \) is absences and \( y \) is exam score. The y - intercept of a linear equation \( y=mx + b \) is the value of \( y \) when \( x = 0 \). So when \( x = 0 \) (zero absences), \( y=80 \). Let's analyze the options:

• Option 1: Incorrect. If \( x = 80 \), \( y=-2\times80 + 80=-80\), not 0.
• Option 2: Correct. When \( x = 0 \) (zero absences), \( y = 80 \), so a student with zero absences is predicted to score 80.
• Option 3: Incorrect. When \( x = 0 \), \( y = 80\), not - 2.
• Option 4: Incorrect. The slope (-2) represents the change in score per absence, not the y - intercept.

Answer:

For each additional hour studied, the predicted test score increases by 5 points.

Second Question (Regression Line Y - Intercept Interpretation)