• Two Variable
• Covariance
• Correlation
• Coefficient
• Linear Regression

The regression line is the line that best fits or represents the data on the scatter plot.

Line of Regression of Y on X

The regression line of y on x is used to estimate the values of y from x.

The slope of the line is the quotient between the covariance and variance of the variable X.

Line of Regression of X on Y

The regression line of x on y is used to estimate the values of x from the values of y.

The slope of the line is the quotient between the covariance and variance of the variable y.

If r = 0 the regression lines are perpendicular to each other, and their equations are:

y =

x =

Example

The scores of 12 students in their mathematics and physics classes are:

Mathematics	2	3	4	4	5	6	6	7	7	8	10	10
Physics	1	3	2	4	4	4	6	4	6	7	9	10

Find the regression lines and represent them.

xi	yi	xi ·yi	xi2	yi2
2	1	2	4	1
3	3	9	9	9
4	2	8	16	4
4	4	16	16	16
5	4	20	25	16
6	4	24	36	16
6	6	36	36	36
7	4	28	49	16
7	6	42	49	36
8	7	56	64	49
10	9	90	100	81
10	10	100	100	100
72	60	431	504	380

1. Find the arithmetic means.

2. Calculate the covariance.

3. Calculate the variances.

4.Linear regression of y on x.

5.Linear regression of x on y.

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