A study of training time x x\,x hours and race improvement y y\,y seconds gives a correlation coefficient of 0.94 and the regression line y=1.8x+2.4y=1.8x+2.4y=1.8x+2.4. The observed point for one athlete is (8,15.1)(8,15.1)(8,15.1).
Describe the association shown by the correlation coefficient.
Calculate the fitted value of y y\,y when x=8x=8x=8 and hence find the residual for this athlete.
Interpret the sign of the residual in context.
Explain why the study does not establish that extra training causes the improvement.
121 exam-style questions on OCR (MEI) A Level Maths 2.2 Data Presentation and Interpretation, covering 2.2.1 Types of data and standard diagrams, 2.2.2 Area in a histogram is proportional to frequency, 2.2.3 Cumulative frequency diagram, 2.2.4 Describe frequency distributions, 2.2.5 Samples and theoretical distributions, 2.2.6 Interpret a scatter diagram, 2.2.7 Distinct sections and outliers in scatter diagrams, 2.2.8 Correlation and causation, 2.2.9 Select or critique data presentation techniques, 2.2.10 Measures of central tendency, 2.2.11 Simple measures of spread, 2.2.12 Variance and standard deviation, 2.2.13 Outliers, 2.2.14 Cleaning data, and 2.2 Data Presentation and Interpretation. Each one has a worked solution and a mark scheme showing where the marks go.