Concept explainers
a.
To solve: the system and write the least square regression parabola for the data using Cramer’s Rule.
a.
Answer to Problem 32E
Solution of the system,
The equation of the least squares regression parabola is,
Explanation of Solution
Given information: The retail sales y (in billions of dollars) of automobile and other
motor vehicle dealers in the U.S from 2013 through 2017 can be expressed by ordered
pairs of the form ( t, y(t )) , where t =3 represents 2013. Ordered pairs are;
(3, 874.3),
(4, 935.1),
(5, 1004.8),
(6, 1053.9),
(7, 1103.4).
The coefficients of the least squares regression parabola
Calculation:
The given system is,
Matrix of Coefficients:
Answer column:
Replace the c −column values with the answer column values:
Replace the b −column values with the answer column values
Replace the a −column values with the answer column values
D denotes the determinant, solve by using Cramer Rule
So, the equation of the least squares regression parabola is,
b.
To graph: the parabola with the data and find how does the model fit the data.
b.
Answer to Problem 32E
The model fits the data well.
Explanation of Solution
Given information: The equation of the least squares regression parabola is,
(3, 874.3),
(4, 935.1),
(5, 1004.8),
(6, 1053.9),
(7, 1103.4).
Calculation:
The graph of the parabola
So, the model fits the data well.
Chapter 7 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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