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 One gas station not included in the table below had a listed price of $2.78 for regular gas. Find the best predicted price of premium gas at this station. Is the result close to the actual price of $2.93 for premium gas?
Answer :
Step 1 of 1 :
Given
Figure
Gas Prices One gas station not included in the table below had a listed price of $2.78 for regular gas.
Given data
x 
y 
2.77 
3.07 
2.77 
3.09 
2.79 
3 
2.81 
3.06 
2.78 
3.03 
2.86 
3.06 
2.75 
3.02 
2.77 
3.03 
Now we have to determine the equation of the regression line.
The table is given below.
x 
y 
xy 

2.77 
3.07 
8.5039 
7.6729 
2.77 
3.09 
8.5593 
7.6729 
2.79 
3 
8.37 
7.7841 
2.81 
3.06 
8.5986 
7.8961 
2.78 
3.03 
8.4234 
7.7284 
2.86 
3.06 
8.7516 
8.1796 
2.75 
3.02 
8.305 
7.5625 
2.77 
3.03 
8.3931 
7.6729 
The formula of the the regression line.
= a + bx
where is the dependent variable (that’s the variable that goes on the Y axis).
x is the independent variable (i.e. it is plotted on the X axis).
b is the slope of the line and a is the yintercept.
Where
a = and
b =
The first step in finding a linear regression equation is to determine if there is a relationship between the two variables.
a =
a =
a =
a = 2.566
b =
b =
b =
b = 0.1717
b 0.172
The formula of the the regression line.
= a + bx
Substitute a = 2.566 and b = 0.172
= 2.566 + 0.172 x
Therefore the regression line is = 2.566 + 0.172 x .
Now we need to find the best predicted price of premium gas at this station.
The formula of the best prediction is
=
The regression line does not fit the data well, so the best predicted value is = $3.05.
The predicted price is not very close to the actual price of $2.93.