# Regression Calculator – Simple/Linear

Regression refers to a statistical that attempts to determine the strength of the relationship between one dependent variable (usually denoted by Y) and a series of other changing variables (known as independent variables). Here the relation between selected values of x and observed values of y (from which the most probable value of y can be predicted for any value of x) are taken into consideration.
Simple/Linear Regression Statistics Calculator
 X Value : Y Value :
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 Total Numbers : Slope (b): y-Intercept(a) : Regression Equation(y) :
Formula
Regression Formula:
Regression Equation(y) = a + bx
Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (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
ΣX2 = Sum of square First Scores
Related Article: A regression is a statistical analysis assessing the association between two variables. The description of the nature of the relationship between two or more variables; it is concerned with the problem of describing or estimating the value of the dependent variable on the basis of one or more independent variables is termed as a statistical regression.

Example:
To find the Simple/Linear Regression of

 X Values Y Values 2 2.1 5 2.6 7 2.8 4 4 8 4.1

Step 1: Count the number of values.
N = 5

Step 2: Find XY, X2
See the below table

 X Value Y Value X*Y X*X 2 2.1 2 * 2.1 = 4.2 2*2 =4 5 2.6 5 * 2.6 = 13 5*5 = 25 7 2.8 7 * 2.8 = 19.6 7*7 =49 4 4 4 * 4 = 16 4*4  = 16 8 4.1 8 * 4.1 = 32.8 8*8 = 64

Step 3: Find ΣX, ΣY, ΣXY, ΣX2.
ΣX = 26
ΣY = 15.6
ΣXY = 85.6
ΣX2 =158

Step 4: Substitute in the above slope formula given.
Slope (b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
= ((5)*(85.6)-(26)*(15.6))/((5)*(158)-(26)2)
= (428 – 405.6)/(790 - 676)
= 22.4/114
= 0.19649

Step 5: Now, again substitute in the above intercept formula given.
Intercept (a) = (ΣY - b(ΣX)) / N
= (15.6 - 0.196(26))/5
= (15.6 – 5.106)/5
= 10.494/5
= 2.0988

Step 6: Then substitute these values in regression equation formula
Regression Equation(y) = a + bx
= 2.0988 + 0.196x.