Question

In: Statistics and Probability

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

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

Solutions

Expert Solution

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.


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