# 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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