For children aged 5 to 12, a study gives the regression line h=6.1a+78h=6.1a+78h=6.1a+78 for predicting height h h\,h cm from age a a\,a years. A separate regression of age on height is a=0.12h−7.9a=0.12h-7.9a=0.12h−7.9.
Use the first regression line to predict the height of a child aged 9 years.
Use the second regression line to predict the age of a child whose height is 135 cm.
Explain why rearranging the first regression line would not, in general, give the second regression line.
State whether each prediction is interpolation or extrapolation, giving a reason.
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.