A garden centre records the age, x x\,x weeks, and the height, y y\,y cm, of each of 20 seedlings of the same variety. The ages in the sample range from 2 weeks to 9 weeks.
The product moment correlation coefficient between x x\,x and y y\,y is 0.94, and the regression line of y y\,y on x x\,x for these data is
y=3.1+2.4xy = 3.1 + 2.4xy=3.1+2.4x
Interpret the value 3.1 in this model, and state, with a reason, whether it is reliable.
A seedling of this variety is 18 cm tall. A student estimates its age as 18−3.12.4=6.2\dfrac{18 - 3.1}{2.4} = 6.22.418−3.1=6.2 weeks. Give one reason why using this equation is not a sound way to estimate the age.
Explain why this model should not be used to estimate the height of a seedling of this variety at 30 weeks.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.