Calculators & Converters

    Correlation between {81, 85, 96, 75, . . . , 75} & {95, 96, 99, 82, . . . , 75}

    Correlation Coefficient CalculatorSolved example problem, work with steps & calculation summary for correlation (r) between {81, 85, 96, 75, . . . , 75} & {95, 96, 99, 82, . . . , 75} 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{81, 85, 96, 75, 65, 90, 82 & 75}
    Data set y{95, 96, 99, 82, 85, 60, 57 & 75}
    Correlation Coefficient (r)0.0763

    Work with Steps for Correlation r = 0.0763

    Question:
    Find the following data X & Y positively or negatively correlated?
    X 81 85 96 75 65 90 82 75
    Y 95 96 99 82 85 60 57 75

    Workout :

    step 1 Address the formula, input parameters and values
    data set x = {81, 85, 96, 75, 65, 90, 82 and 75}
    data set y = {95, 96, 99, 82, 85, 60, 57 and 75}
    Total number of elements (n) = 8

    step 2 Find x̄ & ȳ
    x̄ = 649/8
    x̄ = 81
    ȳ = 649/8
    ȳ = 81

    step 3 To find coefficient correlation follow below the table

    xyX = x - x̄Y = y - ȳX2Y2XY
    8195-0.12513.8750.0156 192.5156-1.7344
    85963.87514.87515.0156 221.265657.6406
    969914.87517.875221.2656 319.5156265.8906
    7582-6.1250.87537.5156 0.7656-5.3594
    6585-16.1253.875260.0156 15.0156-62.4844
    90608.875-21.12578.7656 446.2656-187.4844
    82570.875-24.1250.7656 582.0156-21.1094
    7575-6.125-6.12537.5156 37.515637.5156
    ∑x = 649∑y = 649∑X = 0∑Y = 0∑X2 = 650.875∑Y2 = 1814.875∑XY = 82.875

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

    r = ∑XY∑X2. ∑Y2

    ∑XY = 82.875, ∑X2 = 650.875, ∑Y2 = 1814.875

    r = 82.875650.875 x 1814.875

    step 5 Simplify above expression

    = 82.8751181256.7656

    = 82.8751086.8564

    r = 0.0763

    Thus 0.0763 is the correlation between x = {81, 85, 96, 75, 65, 90, 82 and 75} & y = {95, 96, 99, 82, 85, 60, 57 and 75}

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