Question

1.Is the following statement true or false?

For simple linear regression (i.e., when we predict variable Y only on the basis of variable X), the standardized regression coefficient (β) will be equal to the Pearson correlation coefficient (r).

2.

Please consider the following values for the variables X and Y. Treat each row as a pair of scores for the variables X and Y (with the first row providing the labels "X" and "Y").

X	Y
2	4
4	3
6	5
7	7
11	6

Please calculate Pearson's correlation coefficient (r) for these data and report your answer below. When reporting your answer, please provide three decimal places (if relevant).

Answer 1

Q 1) For simple linear regression, we compute the slope as follows:

Note that

where the first term is equal to r, which we defined earlier; we can now see that we could use the “linear correlation coefficient” to compute the slope of the line as

Note that slope is equal to the correlation coefficient(r) when

So. the given statement is TRUE if ....................(ANSWER)

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6)Correlation Coefficient ( r) can be calculated as

we can calculate it as

Sr. No.	x	y	(x-xbar)	(y-ybar)	(x-xbar)^2	(y-ybar)^2	(x-xbar)*(y-ybar)	(x-xbar)^2*(y-ybar)^2
1	2	4	-4	-1	16	1	4	16
2	4	3	-2	-2	4	4	4	16
3	6	5	0	0	0	0	0	0
4	7	7	1	2	1	4	2	4
5	11	6	5	1	25	1	5	25
Mean	6	5		Total	46	10	15	61

we get

....................(ANSWER)

we get Pearson's correlation coefficient (r) = r = 0.699 ...................(ANSWER)