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Linear Regression Calculator
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A linear regression is a statistical analysis for evaluating the point of contact between two variables. Linear Regression Calculator calculates the linear regression Equation between two given variables.

Linear Regression Definition:
The linear regression is the approach for modelling the relationship with the straight lines in-between the variables through the observed data of linear equation. The linear regression is similar to all the kinds of analysis in regression, it concentrates towards conditional probability distribution of the value 'y' for the given 'x' value rather than joint distributions of x and y, where they are the domain for multi-variate analyse. Between the 2 variables, the scalar y variable is known to be the variable of explanatory and the other n number of variable is denoted by x variable and it is considered as dependent variables.

Linear Regression Formula:
Regression Equation(y) = a + bx
Slope(b) = $\frac{(N\sum{xy} - (\sum{x})(\sum{y}))}{(N\sum{x^{2}} - (\sum{x})^{2})}$
Intercept(a) = $\frac{(\sum{y} - b(\sum{x}))}{N}$

where,
x and y are the given variables
b = Regression line slope
a = Intercept point between regression line and the y-axis
N = Total number of values
x = First data values
y = Second data values
$\sum{xy}$ = Sum of the product of first and second data values
$\sum{x}$ = Sum of first data values
$\sum{y}$ = Sum of second data values
$\sum{x^{2}}$ = Sum of square first data values.

You can see a default number of values for x and y given below. Click on "Submit", it will first calculate the slope and intercepts by putting up the number values in their respected formula and then finally find the regression equation by substituting those resultant values in the formula.

Steps for Linear Regression Calculator

Step 1 :

Find the number of values N.

Step 2 :

Determine the value of xy, x2, Ʃx, Ʃy, Ʃxy and Ʃx2.

Step 3 :

Find the value of a and b using slope and intercept formula.
Slope(b)=[N Ʃxy-(Ʃx)(Ʃy)]/[NƩx2-(Ʃx)2]
Intercepts(a)=[Ʃy-b(Ʃx)]/N

Step 4 :

Substitute a and b value into the equation,
Regression Equation = a+bx

Problems on Linear Regression Calculator

1. Find the regression equation of x values y values 50 2.5 51 3 52 3.5

Step 1 :

Find N = 3

Step 2 :

Find xy and x2

 x values y values xy x*x 50 2.5 125 2500 51 3 153 2601 52 3.5 182 2704

Ʃx = 153
Ʃy = 9
Ʃxy =460
Ʃx2 =7805

Step 3 :

Find slope and intercept

Slope(b)=[N Ʃxy-(Ʃx)(Ʃy)]/[NƩx2-(Ʃx)2]
Slope(b)=[3*460-153*9]/[3*7805-(153)2]
Slope(b)=0.5

Intercepts(a)=[Ʃy-b(Ʃx)]/N
Intercepts(a)=[9-(0.5)*153]/3
Intercepts(a)= -22.5

Step 4 :

Substitute a and b value into the equation,
Regression Equation = a+bx
Regression Equation = -22.5+0.5x
Regression Equation = 0.5x-22.5