Question

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation ŷ = –3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. Which statement best describes the meaning of the y-intercept of the regression line?

AWhen the grade is 0, the predicted number of procrastination days is 0.
BWhen the grade is 0, the predicted number of procrastination days is 96.5.
CWhen the number of procrastination days is 0, the predicted grade is 3.64 points.
DWhen the number of procrastination days is 0, the predicted grade is 96.5 points.

Answer 1

Answer:

The best option is: When the number of procrastination days is 0, the predicted grade is 96.5 points.

Option D is correct option.

Step-by-step explanation:

The regression equation given is: $y= -3.64x + 96.5$

where x represents the number of procrastination days and ŷ is the predicted grade.

Which statement best describes the meaning of the y-intercept of the regression line?

First we need to identify what is y-intercept in regression line.

The y-intercept of the regression line is the value of output y when x is 0.

So, when x = 0, the value of output is y-intercept

So, if x = 0

we get:

$y= -3.64x + 96.5\\y= -3.64(0) + 96.5\\y=0+96.5\\y=96.5$

So, the best option is: When the number of procrastination days is 0, the predicted grade is 96.5 points.

Option D is correct option.