Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 102.In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 105.
Gas Prices Using the data from the preceding exercise, find the best predicted price for midgrade gas for a station that posted $2.78 as the price of regular gas. Is the result close to the actual price of $2.84 for midgrade gas?
Problem 26 BSC
Answer:
Step1 of 3:
We have Exercises use the same data sets as Exercises in Section 102. In each case, find the regression equation, letting the first variable be the predictor (x) variable.
x 
3 
2.77 
2.89 
2.93 
2.93 
2.96 
2.86 
2.91 
y 
3.07 
3.09 
3 
3.06 
3.03 
3.06 
3.02 
3.03 
Step2 of 3:
We need to Find the indicated predicted value by following the prediction procedure summarized in Figure and find the best predicted price for midgrade gas for a station that posted $2.78 as the price of regular gas. Is the result close to the actual price of $2.84 for midgrade gas?
Step3 of 3:
Consider,
x 
y 
xy 

3 
3.07 
9.21 
9 
2.77 
3.09 
8.5593 
7.6729 
2.89 
3 
8.67 
8.3521 
2.93 
3.06 
8.9658 
8.5849 
2.93 
3.03 
8.8779 
8.5849 
2.96 
3.06 
9.0576 
8.7616 
2.86 
3.02 
8.6372 
8.1796 
2.91 
3.03 
8.8173 
8.4681 
23.25 
24.36 
70.7951 
= 67.6041 
the equation of the regression line is given by
Where,
a =
=
=
=
= 3.1439
And
b =
=
=
=
= 0.0340
0.034
Now the regression line is
The best prediction is
=
= 3.045.