Question

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

Answer 1

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.

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