QCAA General Maths EA key terms

Data recorded in pairs on two variables for each individual, so that the relationship between the variables can be examined, for example height and shoe size measured on the same people.

The variable plotted on the horizontal axis that is used to explain or predict changes in the other variable. It is sometimes called the independent variable.

The variable plotted on the vertical axis whose values are thought to depend on, or be predicted by, the explanatory variable. It is sometimes called the dependent variable.

A graph of paired data in which each individual appears as a single point located by its values on the two variables, used to reveal the form, direction and strength of association.

A systematic pattern linking two variables, described by its direction (positive or negative), its form (linear or non-linear) and its strength (strong, moderate or weak).

A number between negative one and one, usually written r, that measures the direction and strength of a linear association; values near the extremes indicate strong linearity.

The square of the correlation coefficient, giving the proportion of the variation in the response variable that is accounted for by the linear relationship with the explanatory variable.

The straight line fitted to bivariate data by minimising the sum of squared vertical distances of points from the line; it is used to predict response values from explanatory values.

The vertical difference between an observed response value and the value predicted by the fitted line at the same explanatory value; positive residuals lie above the line.

A graph of residuals against the explanatory variable, used to check whether a straight line is an appropriate model; random scatter supports linearity while patterns suggest otherwise.

Predicting a response value using an explanatory value that lies within the range of the observed data, which is generally a reliable use of a fitted model.

Predicting a response value using an explanatory value outside the range of the observed data; such predictions are unreliable because the established pattern may no longer hold.

An observation that lies unusually far from the overall pattern of the remaining data, which may strongly influence a fitted line or a correlation coefficient.

A data point whose removal noticeably changes the fitted line, correlation or conclusions of an analysis, often because it has an extreme explanatory value.

A link in which a change in one variable actually produces a change in the other; a strong association alone does not establish causation because of possible confounding.

A variable not included in the study that is associated with both variables being compared, so that an observed association may be partly or wholly explained by it.

A set of values of a single variable recorded at successive, usually equally spaced, times, analysed to reveal trend and seasonal behaviour and to forecast future values.

The long-term underlying direction of a time series once short-term fluctuations are allowed for, described as increasing, decreasing or stable over the period observed.

A number describing how far a particular season or period typically sits above or below the trend, expressed as a proportion or percentage of the trend value.

Removing the seasonal component from a time series by dividing each value by its seasonal index, so that the underlying trend becomes easier to identify.

Averaging neighbouring values of a time series, for example with a moving average, to reduce short-term random and seasonal variation so the trend is clearer.

A sequence of averages, each calculated from a fixed number of consecutive observations, used to smooth a time series; an even number of points requires centring.

Longer-term wave-like movements in a time series that repeat over periods of more than a year, such as economic booms and downturns, distinct from regular seasonal patterns.

The irregular, unpredictable component of a time series that remains after trend, seasonality and cycles are accounted for, often treated as chance fluctuation.

The study of positions and distances on the surface of the Earth using a spherical model, with latitude and longitude measured in degrees and minutes.

A circle on a sphere whose plane passes through the centre, dividing the sphere into two equal halves; the shortest surface path between two points lies on one.

A circle on a sphere whose plane does not pass through the centre, such as a line of latitude other than the equator; it is not the shortest path between points.

The angular distance of a place north or south of the equator, measured in degrees from zero at the equator to ninety at each pole.

The angular distance of a place east or west of the prime meridian, measured in degrees from zero to one hundred and eighty in each direction.

A unit of distance at sea defined as the length of one minute of arc along a great circle of the Earth, approximately one point eight five two kilometres.

A region sharing a common clock time, related to longitude so that each fifteen degrees of longitude corresponds to one hour of time difference from the prime meridian.

The standard reference time against which local times around the world are set, formerly known as Greenwich Mean Time, based on the prime meridian.

A direction measured clockwise from north, written as three digits between zero and three hundred and sixty degrees, used in navigation and surveying.

A bearing measured clockwise from true north, expressed with three digits such as zero four five degrees, so that east is ninety degrees and south is one hundred and eighty.

A direction given as an angle measured from north or south towards east or west, such as north thirty degrees east, which can be converted to a true bearing.

A relationship stating that each side of a triangle divided by the sine of its opposite angle is constant, used to solve non-right-angled triangles when a matching pair is known.

A generalisation of Pythagoras' theorem giving the third side of a triangle from two sides and the included angle, or an angle from all three sides.

For a triangle with two known sides and the included angle, the area equals half the product of the two sides multiplied by the sine of the included angle.

A method of finding the area of a triangle from its three side lengths alone, using the semi-perimeter and the product of the semi-perimeter minus each side.

A surveying method in which distances and bearings are measured from one central point to several others, allowing positions and areas to be calculated by triangle rules.