Question

What is the value of R2 statistics? What does this statistics tell?

	Customers (in 1000s), X	Line Maintenance Expense (in $1000s), Y	X^2	Y^2	XY
	25.3	484.6	640.09	234837.16	12260.38
	36.4	672.3	1324.96	451987.29	24471.72
	37.9	839.4	1436.41	704592.36	31813.26
	45.9	694.9	2106.81	482886.01	31895.91
	53.4	836.4	2851.56	699564.96	44663.76
	66.8	681.9	4462.24	464987.61	45550.92
	78.4	1037	6146.56	1075369	81300.8
	82.6	1095.6	6822.76	1200339.36	90496.56
	93.8	1563.1	8798.44	2443281.61	146618.78
	97.5	1377.9	9506.25	1898608.41	134345.25
	105.7	1711.7	11172.49	2929916.89	180926.69
	124.3	2138.6	15450.49	4573609.96	265827.98
Total	848	13133.4	70719.06	17159980.62	1090172.01

Answer 1

The coefficient of determination (r2) is determined as follows:

S_xx = ?x² – (1/n)(?x)² = 70719.06 – (1/12)(848)² = 10793.73

S_yy = ?y² – (1/n)(?y)² = 17159980.62 – (1/12)(13133.4)² = 2786130.99

S_xy = ?xy – (1/n)(?x)(?y) = 1090172.01 – (1/12)(848)(13133.4) = 162078.41

R² = (S_xy)²/( S_xx * S_yy) = (162078.41)²/(10793.73*2786130.99) = 0.8735

R² = 0.8735

Coefficient of determination, R² explains likelihood of future data points or expenses that fall within the results of predicted outcomes. Thus, for given data 87.35 of added sample data points will fall within the results predicted outcome from the regression line.