Calculators & Converters

    Correlation between {1, 2, 3, 4 & 5} & {2, 1, 4, 3 & 7}

    Correlation Coefficient CalculatorSolved example problem, work with steps & calculation summary for correlation (r) between {1, 2, 3, 4 & 5} & {2, 1, 4, 3 & 7} to estimate the linear relationship or to find if the data linearly, non-linearly, positively or negatively correlated in statistical experiments.
    Calculation Summary
    Data set x{1, 2, 3, 4 & 5}
    Data set y{2, 1, 4, 3 & 7}
    Correlation Coefficient (r)0.8242

    Work with Steps for Correlation r = 0.8242

    Users may refer the below example workout with steps to find if any correlation between dataset x = {1, 2, 3, 4 & 5} & y = {2, 1, 4, 3 & 7} or to learn the input parameters & values are being used in the calculation.

    Workout :

    step 1 Address the formula, input parameters and values
    data set x = {1, 2, 3, 4 and 5}
    data set y = {2, 1, 4, 3 and 7}
    Total number of elements (n) = 5

    step 2 Find x̄ & ȳ
    x̄ = 15/5
    x̄ = 3
    ȳ = 17/5
    ȳ = 3

    step 3 To find coefficient correlation follow below the table

    xyX = x - x̄Y = y - ȳX2Y2XY
    12-2-1.44 1.962.8
    21-1-2.41 5.762.4
    3400.60 0.360
    431-0.41 0.16-0.4
    5723.64 12.967.2
    ∑x = 15∑y = 17∑X = 0∑Y = 0∑X2 = 10∑Y2 = 21.2∑XY = 12

    step 4 Substitute ∑x, ∑y, ∑xy, ∑x2 & ∑y2 value in the below correlation coefficient formula

    r = ∑XY∑X2. ∑Y2

    ∑XY = 12, ∑X2 = 10, ∑Y2 = 21.2

    r = 1210 x 21.2

    step 5 Simplify above expression

    = 12212

    = 1214.5602

    r = 0.8242

    Thus 0.8242 is the correlation between x = {1, 2, 3, 4 and 5} & y = {2, 1, 4, 3 and 7}

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