Question

For the following data set: x| 8,4,6,12,-9,-3,5,-11 y| 4,3,31,59,0,4,-3,-16 A. Use TI 84 calculator to compute the coefficient of determination. round answer to 3 decimal places. B. How much of the variation in the outcome variable that is explained by at least -squares regression line?

Answer 1

(A)

From the given data, the following Table is calculated:

X	Y	XY	X2	Y2
8	4	32	64	16
4	3	12	16	9
6	31	188	36	961
12	59	708	144	3481
- 9	0	0	81	0
- 3	4	- 12	9	16
5	- 3	- 15	25	9
- 11	- 18	176	121	256
Total = 12	82	1087	496	4748

The Correlation Coefficient (r) is given by:

So,

Coefficient of Determination is given by:

R² = 0.7054² = 0.498

So,

Answer is:

0.498

(B)

Percentage of variation in the outcome variable that is explained by least square regression line is given by:

49.8 %