Question 17 (7 points) here is a positive correlation between the amount of time

Question

Question 17 (7 points) here is a positive correlation between the amount of time spent in the cousre esents, for a sample of students in an eCore class, the average and the For online courses, like t the course each week (x) and the overall course grade (y) those in eCore, t number of spent in following table p 345.6 360.1 19.8 135.9 217.3 71.1 Grade 83.6 95 31.5 73.787.1 38.9 Compute the least-squares regression line. rounding ba and b, to two decimal places. Use the least-squares regression line to prediet the course grade of a student in the course who spent an average of 82 minutes in the course each week. Round your answer to one decimal place. Write only a number as your answer Your Ansvwers 11/3

Explanation / Answer

Line of Regression Y on X i.e Y = bo + b1 X

calculation procedure for regression

mean of X = X / n = 191.6333

mean of Y = Y / n = 68.3

(Xi - Mean)^2 = 99906.713

(Yi - Mean)^2 = 3548.18

(Xi-Mean)*(Yi-Mean) = 16902.47

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 16902.47 / 99906.713

= 0.169

bo = Y / n - b1 * X / n

bo = 68.3 - 0.169*191.6333 = 35.879

value of regression equation is, Y = bo + b1 X

Y'=35.879+0.169* X

and for 82 minutes spent the grade value will be

y'=35.879+0.169* 82

= 49.737

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 345.6 83.6 23705.745 234.09 2355.691 360.1 95 28381.029 712.89 4498.061 19.8 31.5 29526.683 1354.24 6323.465 135.9 73.7 3106.201 29.16 -300.96 217.3 87.1 658.779 353.44 482.534 71.1 38.9 14528.276 864.36 3543.679

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