Calculators & Converters

    Correlation between {6.1, 6.0, 5.9, 5.8, . . . , 4.8} & {5.9, 5.7, 6.1, 5.2, . . . , 5.7}

    Correlation Coefficient CalculatorSolved example problem, work with steps & calculation summary for correlation (r) between {6.1, 6.0, 5.9, 5.8, . . . , 4.8} & {5.9, 5.7, 6.1, 5.2, . . . , 5.7} 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{6.1, 6.0, 5.9, 5.8, 5.5, . . . . , 4.9 & 4.8}
    Data set y{5.9, 5.7, 6.1, 5.2, 5.7, . . . . , 4.1 & 5.7}
    Correlation Coefficient (r)0.6328

    Work with Steps for Correlation r = 0.6328

    Question:
    The following data collected from the survey taken at 11 persons. The purpose of this survey is to estimate the height correlation between each father & son in the group. All the measurements are given in feet & inches.
    All the measurement in feet & inches
    Father 6.1 6.0 5.9 5.8 5.5 5.4 5.2 5.1 5.0 4.9 4.8
    Son 5.9 5.7 6.1 5.2 5.7 4.8 5.5 4.3 4.3 4.1 5.7

    Workout :

    step 1 Address the formula, input parameters and values
    data set x = {6.1, 6.0, 5.9, 5.8, 5.5, . . . . , 4.9 and 4.8}
    data set y = {5.9, 5.7, 6.1, 5.2, 5.7, . . . . , 4.1 and 5.7}
    Total number of elements (n) = 11

    step 2 Find x̄ & ȳ
    x̄ = 59.7/11
    x̄ = 5
    ȳ = 57.3/11
    ȳ = 5

    step 3 To find coefficient correlation follow below the table

    xyX = x - x̄Y = y - ȳX2Y2XY
    6.15.90.67270.69090.4525 0.47730.4648
    6.05.70.57270.49090.328 0.2410.2811
    5.96.10.47270.89090.2234 0.79370.4211
    5.85.20.3727-0.00910000000000010.1389 0.0001-0.0034
    5.55.70.07270.49090.0053 0.2410.0357
    5.44.8-0.027299999999999-0.40910.0007 0.16740.0112
    5.25.5-0.22730.29090.0517 0.0846-0.0661
    5.14.3-0.3273-0.90910.1071 0.82650.2975
    5.04.3-0.4273-0.90910.1826 0.82650.3885
    4.94.1-0.5273-1.10910.278 1.23010.5848
    4.85.7-0.62730.49090.3935 0.241-0.3079
    ∑x = 59.7∑y = 57.3∑X = -0.0003∑Y = -0.0001∑X2 = 2.1618∑Y2 = 5.1291∑XY = 2.1073

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

    r = ∑XY∑X2. ∑Y2

    ∑XY = 2.1073, ∑X2 = 2.1618, ∑Y2 = 5.1291

    r = 2.10732.1618 x 5.1291

    step 5 Simplify above expression

    = 2.107311.0882

    = 2.10733.3299

    r = 0.6328

    Thus 0.6328 is the correlation between x = {6.1, 6.0, 5.9, 5.8, 5.5, . . . . , 4.9 and 4.8} & y = {5.9, 5.7, 6.1, 5.2, 5.7, . . . . , 4.1 and 5.7}

    getcalc.com Calculators