## Simple Or Linear Regression Line Tutorial

### Simple Or Linear Regression Line Tutorial

### Regression Definition:

A regression is a statistical analysis assessing the association between two variables. It is used to find the relationship between two variables.

#### Regression Formula:

Regression Equation(y) = a + bx Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX^{2}- (ΣX)

^{2}) Intercept(a) = (ΣY - b(ΣX)) / N

**Where,**

x and y are the variables. b = The slope of the regression line a = The intercept point of the regression line and the y axis. N = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX

^{2}= Sum of square First Scores### Regression Example:

To find the Simple/Linear Regression of

X Values | Y Values |
---|---|

60 | 3.1 |

61 | 3.6 |

62 | 3.8 |

63 | 4 |

65 | 4.1 |

To find regression equation, we will first find slope, intercept and use it to form regression equation.

###### Step 1:

Count the number of values. N = 5

###### Step 2:

Find XY, X

^{2}See the below tableX Value | Y Value | X*Y | X*X |
---|---|---|---|

60 | 3.1 | 60 * 3.1 = 186 | 60 * 60 = 3600 |

61 | 3.6 | 61 * 3.6 = 219.6 | 61 * 61 = 3721 |

62 | 3.8 | 62 * 3.8 = 235.6 | 62 * 62 = 3844 |

63 | 4 | 63 * 4 = 252 | 63 * 63 = 3969 |

65 | 4.1 | 65 * 4.1 = 266.5 | 65 * 65 = 4225 |

###### Step 3:

Find ΣX, ΣY, ΣXY, ΣX

^{2}. ΣX = 311 ΣY = 18.6 ΣXY = 1159.7 ΣX^{2}= 19359###### Step 4:

Substitute in the above slope formula given. Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX

^{2}- (ΣX)^{2}) = ((5)*(1159.7)-(311)*(18.6))/((5)*(19359)-(311)^{2}) = (5798.5 - 5784.6)/(96795 - 96721) = 13.9/74 = 0.19###### Step 5:

Now, again substitute in the above intercept formula given. Intercept(a) = (ΣY - b(ΣX)) / N = (18.6 - 0.19(311))/5 = (18.6 - 59.09)/5 = -40.49/5 = -8.098

###### Step 6:

Then substitute these values in regression equation formula Regression Equation(y) = a + bx = -8.098 + 0.19x. Suppose if we want to know the approximate y value for the variable x = 64. Then we can substitute the value in the above equation. Regression Equation(y) = a + bx = -8.098 + 0.19(64). = -8.098 + 12.16 = 4.06 This example will guide you to find the relationship between two variables by calculating the Regression from the above steps.