Concept explainers
a.
To find: An equation of the regression line.
a.
Answer to Problem 6PPS
The equation of regression line is
Explanation of Solution
Given Information: A table showing the sales at a clothing chain since 2008.
Calculation:
An equation of the best fit line is given by,
- Here, a is the intercept and b is the slope.
The years start from 2008 and go on till 2014.
Assume the year 2008 as 1 and x be the number of years since 2008.
Finding
|
|
|
|
1 | 6.84 | 6.84 | 1 |
2 | 7.6 | 15.2 | 4 |
3 | 10.9 | 32.7 | 9 |
4 | 115.4 | 461.6 | 16 |
5 | 17.6 | 88 | 25 |
6 | 21.2 | 127.2 | 36 |
7 | 26.5 | 185.5 | 49 |
Sum of every column is,
Calculate a as,
Calculate b as,
Substitute the values of a and b in equation (1),
- Here, x be the number of years since 2008.
Hence, the equation of regression line is,
b.
To graph: the residual graph.
b.
Answer to Problem 6PPS
The linear regression model is not a good fit.
Explanation of Solution
Given Information: A table showing the sales at a clothing chain since 2008.
Calculation:
Find the predicted values and error,
|
(observed) |
(predicted) | Residual
(Observed-Predicted) |
1 | 6.84 |
| 5.335 |
2 | 7.6 | 1.55 | 6.05 |
3 | 10.9 | 1.595 | 9.305 |
4 | 115.4 | 1.64 | 113.76 |
5 | 17.6 | 1.685 | 15.915 |
6 | 21.2 | 1.73 | 19.47 |
7 | 26.5 | 1.775 | 24.725 |
The residual graph is,
From the residual plot it is evident that all the residuals are positive and that the linear model is not that a good fit.
Chapter 4 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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