Question

Develop a least-squares estimated regression line. Also, compute the coefficient of determination and explain its meaning.

Price (x)	Units sold (y)
34	4
36	4
32	6
35	5
31	9
38	2
39	1

Answer 1

The following data are passed:

X	Y
34	4
36	4
32	6
35	5
31	9
38	2
39	1

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
	34	4	136	1156	16
	36	4	144	1296	16
	32	6	192	1024	36
	35	5	175	1225	25
	31	9	279	961	81
	38	2	76	1444	4
	39	1	39	1521	1
Sum =	245	31	1041	8627	179

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 = 34.044 - 0.8462 X

Now, the correlation coefficient is computed using the following expression::

Then, the coefficient of determination, or R-Squared coefficient (R^2), is computed by simply squaring the correlation coefficient that was found above. So we get:

Therefore, based on the sample data provided, it is found that the coefficient of determination is R^2 = 0.8925 . This implies that approximately 89.25% of variation in the dependent variable is explained by the independent variable.