Question

the correlation coefficient for the data is ( r = 0.918 ) and ( alpha = 0.05 ). should regression analysis be done?
the regression analysis should not be done.
the regression analysis should be done.
find the equation of the regression line. round the coefficients to at least three decimal places.
( y ^ { prime } = a + b x )
( a = 1.938 )
( b = 0.014 )
find the cost of gasoline when oil is ( $ 58 ) a barrel. round the answer to at least three decimal places.
when oil is ( $ 58 ) a barrel, gas costs( $ ) per gallon.

Explanation:

Step1: Substitute values into regression equation

We have the regression equation \(y'=a + bx\), where \(a = 1.938\), \(b=0.014\), and \(x = 58\).
Substitute \(x = 58\) into the equation: \(y'=1.938+0.014\times58\).

Step2: Calculate the value

First, calculate \(0.014\times58\):
\(0.014\times58=(0.01 + 0.004)\times58=0.01\times58+0.004\times58 = 0.58+0.232 = 0.812\).
Then, calculate \(y'\):
\(y'=1.938+0.812\).

Answer:

\(y'=2.750\)