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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

Table of Contents:

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    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.