Question

Please respond to the short answer items using the below dataset. For any values with long decimals, please round to two decimal places.

X Y

7    16

5 2

6 1

3 2

4    9

What is the value of SP, SS_X, SS_Y, and Pearson correlation r?

For the regression equation Y = bX + a, what is the value of b?

For the regression equation Y = bX + a, what is the value of a?

For the regression equation, using the b and a values you calculated above, what is the expected value of Y when X = 8?

Answer 1

The following data are passed:

X	Y
7	16
5	2
6	1
3	2
4	9

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
	7	16	112	49	256
	5	2	10	25	4
	6	1	6	36	1
	3	2	6	9	4
	4	9	36	16	81
Sum =	25	30	170	135	346

Based on the above table, the following is calculated:

So SP = SSxy = 20

SSX = 10

SSY = 166

pearson correlation is

Now The regression Equation is given by

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

Y=−4+2X

a = -4

b = 2

value of Y when X = 8

Y=−4+2*8 =12 answer