A motoring magazine records the engine size, x x\,x litres, and the carbon dioxide emissions, y y\,y g/km, of a random sample of 24 new petrol cars.
The product moment correlation coefficient between x x\,x and y y\,y is 0.87, and the regression line of y y\,y on x x\,x for these data is
y=118+42.5xy = 118 + 42.5xy=118+42.5x
The engine sizes in the sample range from 1.0 litres to 3.2 litres.
Give an interpretation of the gradient of this regression line.
State, giving a reason, which of the two variables is the explanatory variable.
State, giving a reason, whether the value of the product moment correlation coefficient is consistent with using a linear regression model for these data.
Explain why this model should not be used to estimate the carbon dioxide emissions of a petrol car with an engine size of 6.0 litres.
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.