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

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

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.

Count the number of values. N = 5

Find XY, X^{2}
See the below table

X 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 |

Find ΣX, ΣY, ΣXY, ΣX^{2}.
ΣX = 311
ΣY = 18.6
ΣXY = 1159.7
ΣX^{2} = 19359

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

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

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.

This tutorial will help you dynamically to find the Simple/Linear Regression problems.