Question

Oil and Gas Prices 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 2015.

Oil	$47.79	$44.62	$81.08	$43.67	$40.58	$48.64
Gasoline	2.638	2.636	2.944	2.528	2.623	2.682

1) The correlation coefficient for the data is r = 0.951 and a = 0.01. Should regression analysis be done?

a) The regression analysis should not be done or b) The regression analysis should be done

2) Find the equation of the regression line. Round the coefficients to at least four decimal places.
y'=a+bx

a = _____

b = _____

3) Find the cost of gasoline when oil is $58 a barrel. Round the answer to at least three decimal places.

Cost of gasoline is $ ____

Answer 1

1. The sample size is n=6, so then the number of degrees of freedom is df=n−2=6−2=4

The corresponding critical correlation value rc​ for a significance level of α=0.01, for a two-tailed test is:

rc​=0.917

Observe that in this case, the null hypothesis is rejected if ∣r∣>rc​=0.917.

Here r>rc, so test is significant

b) The regression analysis should be done

2.

Sum of X = 306.38
Sum of Y = 16.051
Mean X = 51.0633
Mean Y = 2.6752
Sum of squares (SS_X) = 1123.6657
Sum of products (SP) = 10.0619

Regression Equation = ŷ = bX + a

b = SP/SS_X = 10.06/1123.67 = 0.0090

a = M_Y - bM_X = 2.68 - (0.01*51.06) = 2.2179

ŷ = 0.0090X + 2.2179

c. For x=58, ŷ = (0.0090*58) + 2.2179=2.740