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Regression Tutorial

  


Regression Definition:
     A regression is a statistical analysis assessing the association between two variables. It is used to find the relationship between two variables.

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 Example: To find the Simple/Linear Regression of

X ValuesY Values
603.1
613.6
623.8
634
654.1


  To find regression equation, we will first find slope, intercept and use it to form regression equation..

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

  Step 2: Find XY, X2
            See the below table


X ValueY ValueX*YX*X
603.160 * 3.1 = 18660 * 60 = 3600
613.661 * 3.6 = 219.661 * 61 = 3721
623.862 * 3.8 = 235.662 * 62 = 3844
63463 * 4 = 25263 * 63 = 3969
654.165 * 4.1 = 266.565 * 65 = 4225


  Step 3: Find ΣX, ΣY, ΣXY, ΣX2.
            ΣX = 311
            ΣY = 18.6
            ΣXY = 1159.7
            ΣX2 = 19359

  Step 4: Substitute in the above slope formula given.
            Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
            = ((5)*(1159.7)-(311)*(18.6))/((5)*(19359)-(311)2)
            = (5798.5 - 5784.6)/(96795 - 96721)
            = 13.9/74
            = 0.19

  Step 5: Now, again substitute in the above intercept formula given.
            Intercept(a) = (ΣY - b(ΣX)) / N
            = (18.6 - 0.19(311))/5
            = (18.6 - 59.09)/5
            = -40.49/5
            = -8.098

  Step 6: Then substitute these values in regression equation formula
            Regression Equation(y) = a + bx
            = -8.098 + 0.19x.

Suppose if we want to know the approximate y value for the variable x = 64. Then we can substitute the value in the above equation.

            Regression Equation(y) = a + bx
            = -8.098 + 0.19(64).
            = -8.098 + 12.16
            = 4.06

This example will guide you to find the relationship between two variables by calculating the Regression from the above steps.



Related Calculator:
>> Simple/Linear Regression Calculator.

This tutorial will help you dynamically to find the Simple/Linear Regression problems.