A professor collected data from one of her classes to investigate the relationship between study time per week

Question

1. What are the least squares regression line for this data

14, 25, 15, 5, 10, 12, 5, 21

GPA: 3.1, 3.7, 3.4, 3.0, 3.1, 3.3, 2.7, 3.8

2.Based on data what is the slope and interpret the meaning in context of this problem

3. based on data what is the y-intercept and interpret its meaning

4. based on data What is the R squared

5. what is the predicted GPA value for 12 hours of study per week?

6. what is the residual for 12 hours of study per week what does this indicate about the regression line at that point?

7. calculate the slope in Y intercept of the line using summary statistics for each of the variable

Answer 1

y^{^}=.047767x + 2.623616

slope meaning is for every increase of weekly study by 1 hour the gpa goes up on average .0447767

y-intercept meaning no hours of study will give result in a a 2.62 gpa

r²=.850394

plug 12 into equation and you will get 3.20

residual at 12 is 3.20-3.30 = -.1

y-intercept is 2.623616