In mathematics, linear regression is the important topics in statistics. The process of determining the relationship between two variables is called as linear regression. It is also one of the statistical analysis methods that can be used to assessing the association between the two different variables. In this article we shall discuss about simple linear regression tutor. Tutor will help the students with step by step solutions for the given problem. The following are the examples involved in simple linear regression tutor.

## Simple linear regression tutor – Formula for Regression:

Here we help to know the regression formulas are

**Formula for regression:**

- Regression Equation(y) = a + bx
- Slope (b) = `(NsumXY – (sumX) (sumY)) / (NsumX^2 – (sum)^2)`
- Intercept(a) = `(sumY – b(sumX)) / N`

Where

x and y are the variables.

b = the slope of the regression line is also called as regression coefficient

a = intercept point of the regression line which is in the y-axis.

N = Number of values or elements

X = First Score

Y = Second Score

`sumXY` = Sum of the product of the first and Second Scores

`sumX` = Sum of First Scores

`sumY` = Sum of Second Scores

`sumX^2` = Sum of square First Scores.

## Simple linear regression tutor – Example problem:

Here we help to solve the example problem in simple linear regression tutor

**Example 1:**

To determine the regression equation by using the regression slope coefficient and intercept value.

X Values |
Y Values |

22 | 14 |

32 | 15 |

42 | 16 |

52 | 17 |

72 | 19 |

For the given data set of data, solve the regression slope and intercept values.

**Solution:**

Let us count the number of values.

N = 5

Determine the values for XY, X^{2 }

X Value |
Y Value |
X*Y |
X*X |

22 | 14 | 308 | 484 |

32 | 15 | 480 | 1024 |

42 | 16 | 672 | 1764 |

52 | 17 | 884 | 2704 |

72 | 19 | 1386 | 5184 |

Determine the following values `sumX` , `sumY` , `sumXY` , `sumX^2` .

`sumX` = 210

`sumY` = 81

`sumXY` = 3730

`sumX^2` = 11160

Substitute values in the slope formula

Slope (b) = `(NsumXY – (sumX) (sumY)) / (NsumX^2 – (sumX)^2)`

= `((5)*(3730)-(210)*(81))/((5)*(11160)-(210)^2)`

= `(18650 – 17010)/ (55800 – 44100)`

= `1640/11700`

b = 0.14

Substitute the values in the intercept formula given.

Intercept (a) = `(sumY – b (sumX)) / N `

= `(81 – 0.14 (210))/5`

= `(81 – 29.4)/5`

= `51.6/5`

a = 10.32

Substitute the Regression coefficient value and intercept value in the regression equation

Regression Equation(y) = a + bx

= 10.32 + 0.14x

**Answer:**

Slope (or) Regression coefficient (b) = 0.14

Intercept (a) = 10.32

Regression equation y = 10.32 + 0.14x