Calculators & Converters

    Correlation between {7000, 7500, 6500, 5000, . . . , 12000} & {5200, 5500, 5750, 4300, . . . , 8300}

    Correlation Coefficient CalculatorSolved example problem, work with steps & calculation summary for correlation (r) between {7000, 7500, 6500, 5000, . . . , 12000} & {5200, 5500, 5750, 4300, . . . , 8300} 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{7000, 7500, 6500, 5000, 7500, 9000, 9500 & 12000}
    Data set y{5200, 5500, 5750, 4300, 6000, 8900, 7200 & 8300}
    Correlation Coefficient (r)0.8572

    Work with Steps for Correlation r = 0.8572

    Question:
    Find the correlation between this below income & expense report.
    Income 7000 7500 6500 5000 7500 9000 9500 12000
    Expense 5200 5500 5750 4300 6000 8900 7200 8300

    Workout :

    step 1 Address the formula, input parameters and values
    data set x = {7000, 7500, 6500, 5000, 7500, 9000, 9500 and 12000}
    data set y = {5200, 5500, 5750, 4300, 6000, 8900, 7200 and 8300}
    Total number of elements (n) = 8

    step 2 Find x̄ & ȳ
    x̄ = 64000/8
    x̄ = 8000
    ȳ = 51150/8
    ȳ = 6394

    step 3 To find coefficient correlation follow below the table

    xyX = x - x̄Y = y - ȳX2Y2XY
    70005200-1000-1193.751000000 1425039.06251193750
    75005500-500-893.75250000 798789.0625446875
    65005750-1500-643.752250000 414414.0625965625
    50004300-3000-2093.759000000 4383789.06256281250
    75006000-500-393.75250000 155039.0625196875
    9000890010002506.251000000 6281289.06252506250
    950072001500806.252250000 650039.06251209375
    12000830040001906.2516000000 3633789.06257625000
    ∑x = 64000∑y = 51150∑X = 0∑Y = 0∑X2 = 32000000∑Y2 = 17742187.5∑XY = 20425000

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

    r = ∑XY∑X2. ∑Y2

    ∑XY = 20425000, ∑X2 = 32000000, ∑Y2 = 17742187.5

    r = 2042500032000000 x 17742187.5

    step 5 Simplify above expression

    = 204250005.6775E+14

    = 2042500023827505.1149

    r = 0.8572

    Thus 0.8572 is the correlation between x = {7000, 7500, 6500, 5000, 7500, 9000, 9500 and 12000} & y = {5200, 5500, 5750, 4300, 6000, 8900, 7200 and 8300}

    getcalc.com Calculators