Question

During a outdoor yoga class, the temperature (?) and the number of absences (?) on 9 randomly selected days are recorded. Find the equation of the least squares regression line for the data below.

Temp. (?) 72 85 91 90 88 98 75 100 80

Absences (?) 4 8 11 12 9 15 3 18 5

(A) ? ̂ = −35.087 + 0.514?

(B) ? ̂ = 0.514 − 35.087?

(C) ? ̂ = 69.209 + 1.837?

(D) ? ̂ = 1.837 + 69.209?

Answer 1

X	Y	XY	X^2	Y^2
72	4	288	5184	16
85	8	680	7225	64
91	11	1001	8281	121
90	12	1080	8100	144
88	9	792	7744	81
98	15	1470	9604	225
75	3	225	5625	9
100	18	1800	10000	324
80	5	400	6400	25

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

n	9
sum(XY)	7736.00
sum(X)	779.00
sum(Y)	85.00
sum(X^2)	68163.00
sum(Y^2)	1009.00

b	0.514488
a	-35.0874

ycap = a+bx

ycap = -35.087 + 0.514x