Concept explainers
a.
To Justify:
The use of a linear function to model the given data set.
The use of a linear function is justified as the data points are clustered near a straight line in the
Given:
The data set:
Year | Fuel Economy (mpg) |
1995 | 21.1 |
2000 | 21.9 |
2005 | 22.1 |
2010 | 23.3 |
2015 | 23.2 |
Assume
Concepts Used:
Drawing of Scatter Plot from data points.
Calculating a linear model that fits the data using a graphing calculator.
Calculations:
Draw a scatter plot of the given data. And fit a regression line on it using a graphing calculator.
It can be seen that the data points are clustered close to a line.
Conclusion:
Thus the use of a linear model is justified.
b.
To Determine:
A linear regression model for the given data set.
To State:
The meaning of the slope in the regression model.
The slope
Given:
The data set:
Year | Fuel Economy (mpg) |
1995 | 21.1 |
2000 | 21.9 |
2005 | 22.1 |
2010 | 23.3 |
2015 | 23.2 |
Assume
Concepts Used:
Drawing of Scatter Plot from data points.
Calculating a linear model that fits the data using a graphing calculator.
The slope
Calculations:
Draw a scatter plot of the given data. And fit a regression line on it using a graphing calculator.
It can be seen that the regression line is
Conclusion:
The regression line is
The slope
c.
To Determine:
The fuel economy in the year
The fuel economy in the year
mpg.
Given:
The data set:
Year | Fuel Economy (mpg) |
1995 | 21.1 |
2000 | 21.9 |
2005 | 22.1 |
2010 | 23.3 |
2015 | 23.2 |
Assume
Known from previous part:
The regression line is
Concepts Used:
Predicting the value of a variable using a linear regression model.
Substitution of a variable.
Calculations:
The year
Substitute
Conclusion:
The fuel economy in the year
mpg.
Chapter 2 Solutions
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
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