Question

Question 9 < > 0/2 pts 399 Details 4 Run a regression analysis on the following data set, where y is the final grade in a math class and x is the average number of hours the student spent working on math each week. hours/week Grade х у 52.6 4 41.6 4 41.6 60 64.6 11 82.4 14 90.6 14 78.6 18 90.2 18 93.2 no State the regression equation y=mx+b, with constants accurate to two decimal places. What is the predicted value for the final grade when a student spends an average of 12 hours each week on math? Grade = Round to 1 decimal place. Question Help: Video Video

Answer 1

From the given data

S.NO.	Hours(x)	Grade(y)	X^2	Y^2	XY
1	4	52.6	16	2766.76	210.4
2	4	41.6	16	1730.56	166.4
3	4	41.6	16	1730.56	166.4
4	5	60	25	3600	300
5	9	64.6	81	4173.16	581.4
6	11	82.4	121	6789.76	906.4
7	14	90.6	196	8208.36	1268.4
8	14	78.6	196	6177.96	1100.4
9	18	90.2	324	8136.04	1623.6
10	18	93.2	324	8686.24	1677.6
Total:	101	695.4	1315	51999.4	8001

Based on the above table, the following is calculated: n X X; 101 10 10.1 n n Y Y 695.4 10 69.54 n SSxx 1315 – 101²/10 = 294.9 SSYY =x*-+ (3x) - w - (3) *xx - (2x) () 51999.4 – 695.42 /10 = 3641.284 SSxy = x;Y; 8001 - 101 x 695.4/10 = 977.46 Therefore, based on the above calculations, the regression coefficients (the slope m, and the y- intercept n) are obtained as follows: m = SSXY SSxx 977.46 294.9 3.3145 n=Y - X.m= 69.54 - 10.1 x 3.3145 = 36.0631 Therefore, we find that the regression equation is: Y = 36.0631 +3.3145 X

The regression equation is y = 3.31X + 36.03

b) Given X = 12 hours

then Y-hat = 3.31(12) + 36.03

= 75.8