The temperature of the water, w ∘Cw\,^{\circ}\text{C}w∘C, in a kettle is recorded t t\,t minutes after the kettle boiled.
ttt: 1, 3, 6, 9, 11, 15, 20
www: 92, 76, 65, 50, 46, 33, 25
The data are coded using the changes of variable x=tx = tx=t and y=log10wy = \log_{10} wy=log10w.
The regression line of y y\,y on x x\,x is found to be
y=1.98−0.0298xy = 1.98 - 0.0298xy=1.98−0.0298x
Given that the data can be modelled by an equation of the form w=abtw = ab^{t}w=abt, where a a\,a and b b\,b are constants, find the value of a a\,a and the value of bbb. Give your answers to 3 significant figures.
Give an interpretation of the constant a a\,a in this model.
Explain why this model is not reliable for predicting the temperature of the water one hour after the kettle boiled.
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.