Simple Regression Formula

Introduction to simple regression formula:

In mathematics, one of the most important topics in statistics is regression. Regression is determining the relationship between two variables. Regression math are used to analysis the several variables. Regression is one of the statistical analysis methods that can be used to assessing the association between the two different variables.

Example of Simple Regression Formula:
Here we study about the simple regression formula are,

Formula for regression analysis:

Regression Equation (y) = a + bx

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

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


Where,
x and y are the variables.
b = the slope of the regression line is also defined as regression coefficient
a = intercept point of the regression line where 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 scores and Second Scores
`(sumX)` = Sum of First Scores
`(sumY)` = Sum of Second Scores
`(sumX^2)` = Sum of square First Scores.

Example Problem for Simple Regression Formula:

Problem for simple regression formula:

Example 1:

Find the regression slope coefficient, intercept value and create a regression equation by using the given table.

X Values   Y Values

10            11

20            22

30            33

40            44

50            55


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, X2

X Value  Y Value    X*Y      X*X

10        11        110      100

20        22        440      400

30        33        990      900

40        44       1760     1600

50        55       2750     2500


Determine the following values `(sumX), (sumY), (sumXY), (sumX^2).`
`(sumX) = 150`
`(sumY)= 165`
`(sumXY)= 6050`
`(sumX^2) = 5500`



Plug values in the slope formula,


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


`= (5 xx(6050)-(150)xx(165))/((5)xx(5500)-(150)^2)`


`= (30250 - 24750)/(27500-22500)`


`= 5500/5000`

`b= 1.1`

Plug the values in the intercept formula,


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


`= (165-(1.1xx150))/5`


`= (165 - 165)/5`


`= 0/5`


`a = 0`

Plug the Regression coefficient values and intercept values in the regression equation,
Regression Equation(y) = a + bx
= 0 + 1.1x

Answer:

Slope (or) Regression coefficient (b) = 1.1

Intercept (y) = 0

Regression equation y = 0 + 1.1x