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.
Sports Using the data from the preceding exercise, find the best predicted volume of a marble with a diameter of 1.50 cm. How does the result compare to the actual volume of 1.8 cm 3?
Problem 28 BSC
Answer:
Step1 of 3:
We have Exercises use the same data sets as Exercises in Section 102. In each case,
x 
7.4 
23.9 
4.3 
21.8 
7 
4 
20.9 
9.7 
y 
212.2 
7148.1 
41.6 
5424.6 
179.6 
33.5 
4780.1 
477.9 
Step2 of 3:
We need to 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.
find the best predicted volume of a marble with a diameter of 1.50 cm. How does the result compare to the actual volume of 1.8 cm3?
Step3 of 3:
Consider,
x 
y 
xy 

7.4 
212.2 
1570.28 
54.76 
23.9 
7148.1 
170839.59 
571.21 
4.3 
41.6 
178.88 
18.49 
21.8 
5424.6 
118256.28 
475.24 
7 
179.6 
1257.2 
49 
4 
33.5 
134 
16 
20.9 
4780.1 
99904.09 
436.81 
9.7 
477.9 
4635.63 
94.09 
99 
18297.6 
396775.95 
=1715.6 
The equation of the regression line is given by
Where,
a =
=
=
=
= 2010.667
And
b =
=
=
=
= 347.302
Now the regression line is
The best prediction is
=
= 2287.2
Therefore,the best predicted volume of a marble with a diameter of 1.50 cm. Is 2287.2c