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x | $X_i$ | $Y_i$ | $X_i^2$ | $X_iY_i$ |
---|---|---|---|---|

1965 | -2 | 125 | 4 | -250 |

1966 | -1 | 140 | 1 | -140 |

1967 | 0 | 165 | 0 | 0 |

1968 | 1 | 195 | 1 | 195 |

1969 | 2 | 200 | 4 | 400 |

N=5 | $\sum X_i=0$ | $ \sum Y_i = 825$ | $ \sum X_i^2=10$ | $\sum X_iY_i=205$ |

The equations are:-

$ \sum Y_i \;=\; Na + b \sum X_i \; \; \therefore 825=5a+b(0) \; \; a \;=\; \dfrac{825}{5} = 165 \\ \; \\ \; \\ \sum X_i Y_i \;=\; a \sum X_i + b \sum X_i^2 \\ \; \\ \; \\ \; \; \; \therefore 205=0a+10b \; \; \; \therefore b\;=\; \dfrac{205}{10} \;=\; 20.5 $

The equation of straight line is $y=a+bX$

$ \\ \; \\ \; \\ \therefore y=165+20.5X \; \; \; where X=x-1967 $

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