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Calcimator

Correlation Calculator

Calculate the Pearson correlation coefficient (r), coefficient of determination (r²), and test significance from summary statistics.

Inputs

Results

Correlation Coefficient (r)

0.47

R-Squared (r²)

0.22

T-Statistic1.51
P-Value (two-tailed, approx)0.15
Degrees of Freedom8
Significant at α=0.05 (1=Yes)0
Strength (0=none, 1=weak, 2=mod, 3=strong, 4=very strong)2
How to Use This Calculator
  1. Enter Number of Data Points (n), Sum of XY (Σxy), and Sum of X (Σx).
  2. Set Sum of Y (Σy), Sum of X² (Σx²), and Sum of Y² (Σy²).
  3. Review Correlation Coefficient (r) and R-Squared (r²).
  4. Use T-Statistic and P-Value (two-tailed, approx) to inform your decision.
  5. Use the chart to visualize the results and explore different scenarios by adjusting inputs.

How the result changes with Sum of XY (Σxy)

Sum of XY (Σxy)Correlation Coefficient (r)R-Squared (r²)
-800,000,000,000-1,714,198,265.22,938,475,692,415,059,000
-300,000,000,000-642,824,354.31413,223,150,495,867,800
300,000,000,000642,824,338.76413,223,130,495,867,840
800,000,000,0001,714,198,249.642,938,475,639,081,725,400

What each input means

Number of Data Points (n)
Total number of paired observations. Must be at least 3.
Sum of XY (Σxy)
Sum of the products of each paired x and y value.
Sum of X (Σx)
Sum of all x values in the data set.
Sum of Y (Σy)
Sum of all y values in the data set.
Sum of X² (Σx²)
Sum of each x value squared.
Sum of Y² (Σy²)
Sum of each y value squared.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Number of Data Points (n) = 10, Sum of XY (Σxy) = 3850, Sum of X (Σx) = 55, Sum of Y (Σy) = 660 = 6 input(s) provided
  2. Calculate Correlation Coefficient
    Correlation Coefficient
    0.4714 = 0.4714
  3. Calculate R-Squared
    R-Squared
    0.2222 = 0.2222
  4. Calculate T-Statistic
    T-Statistic
    1.5119 = 1.5119
  5. Calculate P-Value
    P-Value
    0.154 = 0.154

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators.

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