WJEC Maths for AS: Applied sample

2 Data presentation and interpretation 30 2.3 Making predictions using equations of regression lines You can use the correlation between two variables to make a prediction using the regression line. Prediction makes an estimate of the value of one variable based on the value of another variable. The stronger the correlation between two variables, then the closer the points lie to the regression line, and the more accurate the prediction will be. There are two important terms used: Interpolation is where a value is estimated using the line within the range of the data. So in our beach example you could ϐind the number of people on the beach when the temperature is 22 °C because it lies within the existing data values 5 to 35 °C. Extrapolation is where a value is estimated using the line outside of the range of the data. For example, using the line to ϐind the number of people on the beach when the temperature is −5 °C. The more you extrapolate the less reliable the result is as the data may follow a different trend outside of the range collected You can extrapolate or interpolate using the equation for regression line and substituting in either an x or y value to ϐind the other value. Extrapolation × × × × × × × 0 Length (m) Load (N) Interpolation No readings beyond this point Interpolation – estimates a value wi hin the data range Extrapolation – estimates a value outside the data range L 1 L 2 Correlation does not imply causation If a change in one quantity is accompanied by a change in another quantity they are said to have correlation. However, just because there is correlation between two quantities it does not necessarily mean one quantity causes the other. Linking one thing with another does not always prove that the result has been caused by the other. For example, there is a correlation between the sale of ice cream in America and the number of serious crimes, but you would not say that eating ice cream causes you to commit serious crime. Instead there is another factor – as the temperature goes up people are more irritable and more likely to commit crime. You always have to use common sense deciding whether correlated quantities are causal or not.