Question

The data shown in the table were collected by surveying 100 employees with five years’ experience. Find the correlation relationship for the data. Use Microsoft Excel. Create a scatter plot. Identify and discuss the type of correlation, and whether is negative or positive, strong or weak. Create a regression line and analyze the coefficients for significance. Predict the estimates salary with 20 years of schooling.

Years of schooling	Total annual salary
10	$32 K
12	$33 K
13	$44.3 K
15	$55.7 K
18	$60 K

Answer 1

The scatter plot shows a positive correlation

The following data are passed:

Years of schooling X	Total annual salary ($'k)Y
10	32
12	33
13	44.3
15	55.7
18	60

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	10	32	320	100	1024
	12	33	396	144	1089
	13	44.3	575.9	169	1962.49
	15	55.7	835.5	225	3102.49
	18	60	1080	324	3600
Sum =	68	225	3207.4	962	10777.98

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

Y = -8.8882 + 3.9624 X

At X = 20

Y = -8.8882 + 3.9624 *20

Y = -8.8882 + 79.248

Y = $70.3598 k

Graphically: