Regression formula for y on x

Linear Regression

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x1346891114
y12445789
regression data

From the given data find the regression line of y on x. Estimate value of y when x = 10.

Find function y = f (x)

 Y = f(x) = a + bx ( equation of line y = mx+c )

Y = f(x) = a + bx, is the line of regression of y on x

When a & b are given by the following equations

Regression formula for y on x
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Where as;

Regression formula variables

Now you have to calculate the values which are going to be required in the above equations such as;

  • sum of all x values
  • sum of all y values
  • sum of product of x and y
xyxyx2
1111
3269
441616
642436
854064
976381
11888121
149126196
x=56y=40xy=364x2=524
Regression table y on x

Now put these values in the equation 1 and 2, we get

8a + 56b = 40,   ( eq. 1 )

56a + 542b = 360   ( eq. 2 )

Now, you need to find the value of a and b in these two equations by simplifying them.

We get, a = 6/11 and b = 7/11

Therefore the equation becomes y = 6/11 + (7/11)x

Suggestion:

  1. Newtons Interpolation
  2. Lagrange’s Interpolation
  3. Bisection method
  4. Regula falsi method

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