A retailer records advertising spend x x\,x thousand pounds and weekly sales y y\,y thousand pounds for branches in two regions. The data form two distinct clusters. The fitted lines are y=2.4x+18y=2.4x+18y=2.4x+18 for region A and y=1.1x+42y=1.1x+42y=1.1x+42 for region B. In both regions the observed values of x x\,x lie between 5 and 20.
For each region, estimate weekly sales when advertising spend is £12 000.
Compare the effect of an additional £1000 of advertising spend in the two models.
Explain why fitting one regression line to all the branches could be misleading.
A branch in region A plans to spend £30 000. Explain why its predicted sales should be treated cautiously.
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.