Question

The average gasoline price per gallon (in cities) and the cost of a barrel of oil are shown below

for a random selection of weeks from 2009–2010. Let the x variable be amount of oil and the y

variable be the amount of gasoline. Given that r = 0.9835, Sx = 19.24, Sy = 0.435.

Oil ($) 46.25 37.51 78.00 75.39 84.88 73.78

Gasoline ($) 2.197 2.182 2.987 3.015 3.109 3.000

Find the equation for the regression line.

Answer 1

Solution :

X	Y	XY	X^2	Y^2
46.25	2.197	101.6113	2139.063	4.826809
37.51	2.182	81.84682	1407	4.761124
78	2.987	232.986	6084	8.922169
75.39	3.015	227.3009	5683.652	9.090225
84.88	3.109	263.8919	7204.614	9.665881
73.78	3	221.34	5443.488	9

b = ΠΣxy - (Σx)(ΣΥ) ΠΣχ2 - (Σx)2
  
a = Σy - bΣΧ n

n	6
sum(XY)	1128.98
sum(X)	395.81
sum(Y)	16.49
sum(X^2)	27961.82
sum(Y^2)	46.27
Numerator	246.95
Denominator	251.09
r	0.9835
r square	0.9673
Xbar(mean)	65.9683
Ybar(mean)	2.7483
SD(X)	17.5637
SD(Y)	0.3971
b	0.0222
a	1.2814

The equation for the regression line,

$\hat y$ = a + bx

$\hat y$ = 1.28 + 0.02x