Question
In: Statistics and Probability
The data in the table below show years of teaching experience and annual salary in dollars...
The data in the table below show years of teaching experience and annual salary in dollars for 12 randomly selected mathematics instructors in Illinois colleges/ universities for the 2013-2014 school year. Is there a linear correlation between a mathematics instructor's years of experience and their annual salary?
a. Draw the scatterplot for the variables.
b. Describe the relationship, if any, shown by the scatterplot.
c. Calculate r, the correlation coefficient. How does the correlation coefficient compare to the relationship you saw in the scatterplot?
Number of years: 7 9 6 7 11 12 11 3 3 7 9 1
Salary(in dollars): 48,897 62,866 54,585 56,611 53,541 53,541 47,027 47,970 46,668 48,029 46,735 45,000
Solutions
Expert Solution
a. The scatter plot is given below:
b. There seems to some weak positive linear relationship between the two variables : Number of years and Salary(in dollars)
c.
The provided data are shown in the table below
| X | Y |
| 7 | 48897 |
| 9 | 62866 |
| 6 | 54585 |
| 7 | 56611 |
| 11 | 53541 |
| 12 | 53541 |
| 11 | 47027 |
| 3 | 47970 |
| 3 | 46668 |
| 7 | 48029 |
| 9 | 46735 |
| 1 | 45000 |
Also, the following calculations are needed to compute the correlation coefficient:
| X | Y | X*Y | X2 | Y2 | |
| 7 | 48897 | 342279 | 49 | 2390916609 | |
| 9 | 62866 | 565794 | 81 | 3952133956 | |
| 6 | 54585 | 327510 | 36 | 2979522225 | |
| 7 | 56611 | 396277 | 49 | 3204805321 | |
| 11 | 53541 | 588951 | 121 | 2866638681 | |
| 12 | 53541 | 642492 | 144 | 2866638681 | |
| 11 | 47027 | 517297 | 121 | 2211538729 | |
| 3 | 47970 | 143910 | 9 | 2301120900 | |
| 3 | 46668 | 140004 | 9 | 2177902224 | |
| 7 | 48029 | 336203 | 49 | 2306784841 | |
| 9 | 46735 | 420615 | 81 | 2184160225 | |
| 1 | 45000 | 45000 | 1 | 2025000000 | |
| Sum = | 86 | 611470 | 4466332 | 750 | 31467162392 |
The correlation coefficient r is computed using the following expression:
Therefore, based on this information, the sample correlation coefficient is computed as follows
the correlation coefficient is in line with the relationship seen in the scatterplot - a weak positive association.
Please let me know in comments if anything is unclear. Will reply ASAP. Please upvote if satisfied!
orchestra answered 2 years agoRelated Solutions
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