## Simple Linear Regression From sum and sum of squares

Use this calculator to fit a simple linear regression model from summarized data.

Simple Linear Regression | |
---|---|

No. of Pairs of Observations ($n$) | |

Sum of X : ($\sum x$) | |

Sum of Y : ($\sum y$) | |

Sum of X squares : ($\sum x^2$) | |

Sum of Y squares : ($\sum y^2$) | |

Sum of product of X and Y : ($\sum xy$) | |

Results | |

Mean of X ($\overline{x}$) | |

Mean of Y ($\overline{y}$) | |

Sxx ($S_{xx}$) | |

Syy ($S_{yy}$) | |

Sxy ($S_{xy}$) | |

Correlation between X and Y ($r$) | |

Intercept ($\hat{\beta}_0$) | |

Slope ($\hat{\beta}_1$) | |

Regression equation | |

## Simple Linear Regression

Another method

```
$$
\begin{aligned}
S_{xx}=\sum_{i=1}^n x_i^2- \frac{(\sum_i x_i)^2}{n}
\end{aligned}
$$
```

```
$$
\begin{aligned}
S_{xy}=\sum_{i=1}^n x_iy_i- \frac{(\sum_i x_i)(\sum_i y_i)}{n}
\end{aligned}
$$
```

```
$$
\begin{aligned}
b=\frac{S_{xy}}{S_{xx}}
\end{aligned}
$$
```

```
$$
\begin{aligned}
a=\overline{y}-b \overline{x}
\end{aligned}
$$
```