Concept explainers
To find: An equation of the regression line and the
Answer to Problem 5PPS
The equation of best line is
The
Explanation of Solution
Given Information: A table showing the number of annual violin auditions held by a youth symphony each year since 2009.
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 2009 and go on till 2015.
Assume the year 2009 as 1 and x be the number of years since 2009.
Finding
1 | 22 | 22 | 1 |
2 | 19 | 38 | 4 |
3 | 25 | 75 | 9 |
4 | 37 | 148 | 16 |
5 | 32 | 160 | 25 |
6 | 35 | 210 | 36 |
7 | 42 | 294 | 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 2009.
Hence, the equation of best line is,
Find
1 | 22 | 22 | 1 | 484 |
2 | 19 | 38 | 4 | 361 |
3 | 25 | 75 | 9 | 625 |
4 | 37 | 148 | 16 | 1369 |
5 | 32 | 160 | 25 | 1024 |
6 | 35 | 210 | 36 | 1225 |
7 | 42 | 294 | 49 | 1764 |
Sum of every column is,
Calculate r as,
Therefore, the correlation coefficient is 0.9007
The correlation coefficient lies between
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