Question

Run a regression analysis on the following data set, where yy is the final grade in a math class and xx is the average number of hours the student spent working on math each week.

hours/week x	Grade y
5	56
6	51.4
6	66.4
9	65.6
11	74.4
11	64.4
11	76.4
12	78.8
13	75.2
20	100

State the regression equation y=m⋅x+by=m⋅x+b, with constants accurate to two decimal places.
   

What is the predicted value for the final grade when a student spends an average of 9 hours each week on math?
Grade =  Round to 1 decimal place.

Answer 1

X	Y	XY	X^2	Y^2
5	56	280	25	3136
6	51.4	308.4	36	2641.96
6	66.4	398.4	36	4408.96
9	65.6	590.4	81	4303.36
11	74.4	818.4	121	5535.36
11	64.4	708.4	121	4147.36
11	76.4	840.4	121	5836.96
12	78.8	945.6	144	6209.44
13	75.2	977.6	169	5655.04
20	100	2000	400	10000

From the above table and formula we get the value are as:

n	10
sum(XY)	7867.60
sum(X)	104.00
sum(Y)	708.60
sum(X^2)	1254.00
sum(Y^2)	51874.44

b	2.89
a	40.81

ycap = mx + b

yacp = 2.89 * x + 40.81

when x = 9

Predicted value = 2.89 * 9 + 40.81

= 66.8