WJEC Maths for AS: Applied sample

2.2 Scatter diagrams and regression lines 29 Answer 1 (a) and (b) 160 140 120 100 80 60 40 20 5 10 15 20 25 30 35 40 45 50 Temperature (°C) Visitor number × × × × × × × 0 Using the regression equation The regression equation can be used to calculate one value of a variable given the value of the other variable. However, the regression equation must be used with caution. We only know that the values lie on an approximate straight line between the range of the data values. If we extrapolate (i.e. obtain values outside the range of the data) we are making the assumption that the regression line is true for all the values, which may not be the case. Take the example of people on the beach – we could use the regression equation to calculate the number of people on the beach when the temperature rose to 100 °C (which is impossible). The line passes through (0, 0) and (45, 120) which gives a gradient of 2.78. The regression equation for the line above is y = 2.78 x . So if x = 100, y = 2.78 × 100 = 278 when in fact no-one would be at the beach, as at those temperatures they would all be dead!