Question

For online courses, like those in eCore, there is a positive correlation between the amount of time spent in the course and the course grade. The following table presents, for a sample of students in an eCore class, the average number of minutes spent in the course each week (x) and the overall course grade (y). Minutes 345.6 360.1 19.8 135.9 217.3 71.1 Grade 83.6 95 31.5 73.7 87.1 6.3 Compute the least-squares regression line, rounding b0 and b1 to two decimal places. Use the least-squares regression line to predict the course grade of a student in the course who spent an average of 103 minutes in the course each week. Round your answer to one decimal place. Write only a number as your answer.

Answer 1

Answer:

Regression Line is given by,

y = 22.909 + 0.209 x

The course grade of a student in the course who spent an average of 103 minutes in the course each week is: 22.909 + 0.209 × 103 = 44.436

Step-by-step explanation:

The equation of Regression equation is of the form of:

y = a + bx

where, a is intercept and b is slope

The formula for a and b is given by,

$a=\frac{\sum Y \sum X^2-\sum X \sum XY}{n\sum X^2-(\sum X)^2}\\ and, b = \frac{n\sum XY -\sum X \sum Y}{n\sum X^2-(\sum X)^2}$

Here, ∑X = 1149.8, ∑Y = 377.2, ∑XY = 93115.95, ∑X² = 320246.72

Thus, a = 22.909

and b = 0.209

Thus, Regression Line is given by,

y = 22.909 + 0.209 x

Thus, The course grade of a student in the course who spent an average of 103 minutes in the course each week is: 22.909 + 0.209 × 103 = 44.436

Now plotting these line: