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Concept explainers
a
To find: An equation for the regression line. Letx represents the number of years since 2010.
a
![Check Mark](/static/check-mark.png)
Answer to Problem 23PFA
The equation of regression line is y=250.4x+1002.6 . .
Explanation of Solution
Given information: The table shows U.S. online sales, in millions of dollars ,on Cyber .
Monday since 2010.
Let x be the number of years since 2010.
Years x | 0 | 1 | 2 | 3 | 4 |
Sales y | 1028 | 1251 | 1465 | 1735 | 2038 |
Calculation:
Use a graphing calculator for above table ,
Equation of regression line is,
Sum of X=10.Sum of Y=7515 .Mean X=2.Mean Y=1503.4.Sum of squares(SSX)=10.Sum of products(SP)=2504.Regression equation y=aX+b.a=SP/SSX=2504/10=250.4.b=MY−aMX=1503.4−(250.4×2)=1002.6y=250.4x+1002.6 .
The equation of regression line is y=250.4x+1002.6 .
b
To predict: The Cyber Monday sales in 2025.
b
![Check Mark](/static/check-mark.png)
Answer to Problem 23PFA
Cyber Monday sales in 2025 is 4758.6.
Explanation of Solution
Given information: The table shows U.S. online sales, in millions of dollars ,on Cyber .
Monday since 2010.
Let x be the number of years since 2010.
Years x | 0 | 1 | 2 | 3 | 4 |
Sales y | 1028 | 1251 | 1465 | 1735 | 2038 |
Calculation:
Use a graphing calculator for above table ,
Equation of regression line is,
Sum of X=10.Sum of Y=7515 .Mean X=2.Mean Y=1503.4.Sum of squares(SSX)=10.Sum of products(SP)=2504.Regression equation y=aX+b.a=SP/SSX=2504/10=250.4.b=MY−aMX=1503.4−(250.4×2)=1002.6y=250.4x+1002.6 .........(1).
The equation of regression line is y=250.4x+1002.6 . .
For calculating Cyber Monday sales in 2025, substitutingx =2025-2010=15 in equation (1),
y=250.4x+1002.6 .x=15.y=250.4×15+1002.6.y=3756+1002.6=4758.6.
Cyber Monday sales in 2025 is 4758.6.
c
To find: The
c
![Check Mark](/static/check-mark.png)
Answer to Problem 23PFA
Correlation −coefficient is 0.89010509790.
Explanation of Solution
Given information: The table shows U.S. online sales, in millions of dollars ,on Cyber .
Monday since 2010.
Let x be the number of years since 2010.
Years x | 0 | 1 | 2 | 3 | 4 |
Sales y | 1028 | 1251 | 1465 | 1735 | 2038 |
Calculation:
Use a graphing calculator for above table ,
Equation of regression line is,
Sum of X=10.Sum of Y=7515 .Mean X=2.Mean Y=1503.4.Sum of squares(SSX)=10.Sum of products(SP)=2504.Regression equation y=aX+b.a=SP/SSX=2504/10=250.4.b=MY−aMX=1503.4−(250.4×2)=1002.6y=250.4x+1002.6 .........(1).
The equation of regression line is y=250.4x+1002.6 . .
For calculating Cyber Monday sales in 2025, substitutingx =2025-2010=15 in equation (1),
y=250.4x+1002.6 .x=15.y=250.4×15+1002.6.y=3756+1002.6=4758.6.
Cyber Monday sales in 2025 is 4758.6.
Use a graphing calculator for above table ,
The correlation −coefficient is 0.89010509790.
d
A classmate says that the
d
![Check Mark](/static/check-mark.png)
Answer to Problem 23PFA
No, not agree with your class mate because correlation coefficient is 0.845 which is close to 1 not close to 0, indicates that’s the best-fit line model the data well.
Explanation of Solution
Given information: The table shows U.S. online sales, in millions of dollars ,on Cyber .
Monday since 2010.
Let x be the number of years since 2010.
Years x | 0 | 1 | 2 | 3 | 4 |
Sales y | 1028 | 1251 | 1465 | 1735 | 2038 |
Calculation:
Use a graphing calculator for above table ,
Equation of regression line is,
Sum of X=10.Sum of Y=7515 .Mean X=2.Mean Y=1503.4.Sum of squares(SSX)=10.Sum of products(SP)=2504.Regression equation y=aX+b.a=SP/SSX=2504/10=250.4.b=MY−aMX=1503.4−(250.4×2)=1002.6y=250.4x+1002.6 .........(1).
The equation of regression line is y=250.4x+1002.6 . .
For calculating Cyber Monday sales in 2025, substitutingx =2025-2010=15 in equation (1),
y=250.4x+1002.6 .x=15.y=250.4×15+1002.6.y=3756+1002.6=4758.6.
Cyber Monday sales in 2025 is 4758.6.
Use a graphing calculator for above table ,
The correlation −coefficient is 0.89010509790.
The correlation coefficient is 0.845 which is close to 1 not close to 0, indicates that’s the best-fit line model the data well.
Chapter 4 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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