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Linear Regression Calculator
To find the regression equation, enter the values of x & y coordinates, and click the calculate button using regression calculator
Table of Contents:
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
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.
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
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