Concept explainers
a.
Find an equation for the regression line. Letx represents the number of years since 2006.
a.
Answer to Problem 22PFA
The equation of regression line is
Explanation of Solution
Given information: The table shows the average cost of a 10-person Thanksgiving dinner.
Years | 2006 | 2008 | 2010 | 2012 | 2014 |
Cost($) | 38.10 | 44.61 | 43.47 | 43.48 | 49.41 |
Calculation:
Formula used:
The equation for the regression line is given below.
Let x be the number of years since 2006.So the given table becomes.
Years x | 0 | 2 | 4 | 6 | 8 |
Cost($) y | 38.10 | 44.61 | 43.47 | 43.48 | 49.41 |
Use a graphing calculator for above table,
Equation of regression line is,
The equation of regression line is
b.
Which of the following statements are true.
A −The
B-The average cost in 2009 was about $43.64.
C-The average cost in 2026 was about $75.25.
b.
Answer to Problem 22PFA
A-False.
B-True.
C-False.
Explanation of Solution
Given information: The table shows the average cost of a 10-person Thanksgiving dinner.
Years | 2006 | 2008 | 2010 | 2012 | 2014 |
Cost($) | 38.10 | 44.61 | 43.47 | 43.48 | 49.41 |
Calculation:
Formula used:
The equation for the regression line is given below.
Let x be the number of years since 2006.So the given table becomes.
Years x | 0 | 2 | 4 | 6 | 8 |
Cost($) y | 38.10 | 44.61 | 43.47 | 43.48 | 49.41 |
Use a graphing calculator for above table ,
Equation of regression line is,
The equation of regression line is
Use a graphing calculator for above table,
The
The correlation coefficient is 0.845 which is close to 1 indicates that’s the best-fit line model the data well.
For calculating average cost in 2009, substitutingx =2009-2006=3 in equation (1),
The average cost in 2009 was about $43.64.So B-statement is True.
For calculating average cost in 2026, substitutingx =2026-2006=20 in equation (1),
The average cost in 2026 was about $67.01Which is not $75.25. So C-statement is False.
Chapter 4 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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