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## Linear Regression

x | 1 | 3 | 4 | 6 | 8 | 9 | 11 | 14 |

y | 1 | 2 | 4 | 4 | 5 | 7 | 8 | 9 |

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 )

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

When **a & b** are given by the following equations

Where as;

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

x | y | xy | x^{2} |
---|---|---|---|

1 | 1 | 1 | 1 |

3 | 2 | 6 | 9 |

4 | 4 | 16 | 16 |

6 | 4 | 24 | 36 |

8 | 5 | 40 | 64 |

9 | 7 | 63 | 81 |

11 | 8 | 88 | 121 |

14 | 9 | 126 | 196 |

∑x=56 | ∑y=40 | ∑xy=364 | ∑x^{2}=524 |

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.

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

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

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