Question

Participant	Stress Level (X)	Test Score (Y)
1	18	6
2	3	17
3	12	9
4	8	22
5	15	7
6	7	11

What's the slope of this data (round to two decimal places)?

What's the Y intercept (round to two decimal places)?

What's the predicted test score for a stress level of 10 (round to two decimal places)?

What's the error of participant 5's score (round to two decimal places)?

What's the standard error of the estimate?

What is the coefficient of determination?

Answer 1

X	Y	XY	X^2	Y^2
18	6	108	324	36
3	17	51	9	289
12	9	108	144	81
8	22	176	64	484
15	7	105	225	49
7	11	77	49	121

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

n	6
sum(XY)	625.00
sum(X)	63.00
sum(Y)	72.00
sum(X^2)	815.00
sum(Y^2)	1060.00
Numerator	-786.00
Denominator	1040.72
r	-0.7552

b	-0.8534
a	20.9609

Slope of the dats is -0.85

y intercept is 20.96

When x = 10

predicted test score = 20.96 - 0.85 * 10

= 12.46

X Y XY X^2 Y^2 Ycap (Ycap-Ybar)^2 (Y-Ycap)^2 18 6 108 324 36 5.59934853 40.9683 0.1605 3 17 51 9 289 18.4006515 40.9683 1.9618 12 9 108 144 81 10.7198697 1.6387 2.9580 8 22 176 64 484 14.1335505 4.5520 61.8810 15 7 105 225 49 8.15960912 14.7486 1.3447 7 11 77 49 121 14.9869707 8.9220 15.8959

From the above table we get the value are as;

Error of participants 5 = 1.3447

Standard error of estimate = sqrt(14.0337) = 3.7462

Coefficient of determination formula are as:

From the above calculated table and value we get,

r = -0.7552