Question

The values of y and their corresponding values of y are shown in the table below

x	2	3	4	4	6
y	2	3	5	4	6

A) Calculate the coefficient of correlation;

B) Calculate the coefficient of determination;

C) Obtain the regression coefficients and write the regression expression;

D) Provide your prediction of the dependent variable if the value of the independent variable is 4.

Answer 1

a)

Obs.	X	Y
1	2	2
2	3	3
3	4	5
4	4	4
5	6	6

Now, with the provided sample data, we need to construct the following table to compute the correlation coefficient:

Obs.	X	Y	X_i^2	Y_i^2	Xi​Yi​
1	2	2	4	4	4
2	3	3	9	9	9
3	4	5	16	25	20
4	4	4	16	16	16
5	6	6	36	36	36
Sum =	19	20	81	90	85

Based on the table above, we compute the following sum of squares that will be used in the calculation of the correlation coefficient:

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

b)

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 = 0.9205. This implies that approximately 92.05 of variation in the dependent variable is explained by the independent variable.

c)

Therefore, we find that the regression equation is:

Y = 0.1136 + 1.0227 X

d)

Prediction of y when x = 4.

Y = 0.1136 + 1.0227 *(4)

Y = 0.1136 + 4.0908‬

Y = 4.2044

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