Relationship Measures Calculators
This page presents tools that summarise how variables move together, providing numerical values that describe strength, direction and consistency across datasets.
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Coefficient of Determination (R2) Calculator
The strength of a straight-line relationship between two variables can be summarised by how much of the variation in the response is explained by the predictor.
Example use: checking how well daily temperature predicts the number of minutes spent outdoors.
Inputs: predictor values, response values
Outputs: coefficient of determination, total sum of squares, regression sum of squares, error sum of squares, mean of the response, slope, intercept, total observations
Visual: a scatter display of the data with a fitted straight line showing the overall trend
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Coefficient of Variation Calculator
The relative amount of variation in a dataset can be described by comparing its spread with its average.
Example use: assessing how consistent daily step counts are over a week.
Inputs: dataset values, chosen data type
Outputs: mean, standard deviation, coefficient of variation, squared coefficient of variation, relative standard error, variance-to-mean ratio, number of data points
Visual: a bar display of the actual values with a horizontal line marking the mean
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Correlation Directional Index Calculator
The consistency of movement between two variables can be assessed by counting how often they rise or fall together.
Example use: checking whether the number of minutes spent reading tends to increase on days when the number of pages read also increases.
Inputs: predictor values, response values
Outputs: correlation directional index, total data pairs, valid pairs, directional matches, divergent pairs, co-positive matches, co-negative matches, directional analysis, sign test significance value
Visual: a scatter display of paired observations with a trend line showing the general direction
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Covariance Calculator
The joint variation of two variables can be described by measuring whether large values of one tend to occur with large or small values of the other.
Example use: checking whether the number of minutes spent tidying a room tends to increase on days when the amount of clutter is higher.
Inputs: predictor values, response values, chosen covariance type
Outputs: dataset size, mean of predictor values, mean of response values, sum of products, covariance, correlation coefficient, coefficient of determination, standard error of estimate, regression equation
Visual: a scatter display with markers for each data point and a fitted straight line
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Prediction Efficiency Index (PEI) Calculator
The accuracy of predicted values can be summarised by comparing them with observed values and examining how closely they match in direction and size.
Example use: checking how well predicted daily water intake matches the amount actually consumed.
Inputs: predicted values, observed values
Outputs: prediction efficiency index, theils u2 statistic, bias proportion, directional agreement ratio, prediction directional index, residual sign ratio, total observations
Visual: a scatter display comparing observed and predicted values with a diagonal line showing perfect agreement
Relationship Measures FAQs
Relationship measures quantify how variables interact, indicating strength, direction and consistency across observed numerical changes.
The Coefficient of Variation compares spread relative to the average, helping standardise variation across datasets with different scales.
A positive covariance indicates that both variables tend to rise together, reflecting movement in the same general direction.
The R² value summarises how much variation in an outcome is linked to predictors, indicating overall alignment between model and data.
Prediction efficiency compares model errors with baseline errors, generating a score that reflects improvement over simple averaging.