A retailer records its weekly spending on online advertising, x x\,x hundreds of pounds, and the number of online orders, yyy, for a random sample of 24 weeks.
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 advertising spending in the sample ranges from 1.0 to 3.2 hundreds of pounds.
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 number of online orders in a week when 600 pounds is spent on online advertising.
121 exam-style questions on OCR A Level Maths 2.2 Data Presentation and Interpretation, covering 2.2.1 Tables and diagrams for single variable data, 2.2.2 Area in a histogram, 2.2.3 Scatter diagrams and regression lines, 2.2.4 Informal interpretation of correlation, 2.2.5 Correlation and causation, 2.2.6 Measures of average and spread, 2.2.7 Calculations of mean and standard deviation, 2.2.8 Outliers, 2.2.9 Selecting or critiquing data presentation, and 2.2.10 Cleaning data. Each one has a worked solution and a mark scheme showing where the marks go.