Bivariate Data - Vocabulary

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Correlation

Back

A measure of the strength of the linear relationship between two variables.

Often used interchangeably with association, especially for linear relationships between numerical variables.

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Causation

Back

A relationship where a change in the explanatory variable causes a change in the response variable.

Correlation does not imply causation as there could be a lurking/confounding variable.

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Confounding Variable

Back

A third factor that is responsible for the association between variables.

Also called the Lurking Variable.

Eg. Drowning deaths and ice cream sales are associated. The confounding variable is hot weather.

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Coefficient of determination r²

Back

Tells us what proportion of the variation in y can be explained by the variation in x.

Equal to he correlation coefficient, r, squared.

If r = 0.765, then R² = 0.765² = 0.5852, explaining 59% of variation.

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Explanatory Variable (EV)

Back

A variable that is believed to explain changes in the response variable.

Eg. A study was conducted on speed limits and number of road fatalities.

EV: Speed limits

RV: No. of road fatalities

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Scatterplots

Back

A data display of bivariate numerical data. Each dot represents a single case.

Used to identify associations between two numerical variables.

Conventionally the EV is plotted on the x-axis and the RV on the y-axis.

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Uncontrolled Variables

Back

Variables that can affect the response variable but are not accounted for in the study.

Front

Interpreting the gradient, a, of the regression line

y=ax+b

Back

Explain the meaning of the gradient in the context of the study.

A gradient of (a) tells us that each _______(EV) the ________(RV) increases/decreases by _______(a)

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Extrapolation

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Occurs when predictions are made using values of the explanatory variable outside the range of the original data.

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Residual values

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The difference between the observed value and the value predicted by using the equation for the line of best fit.