Bivariate data, correlation and regressionEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

What does a scatter diagram show?
Which axis does the explanatory variable go on?
What does the gradient of a regression line represent?
What is interpolation?
What is extrapolation?
Linear form of y=ax^n?
For y=ax^n, what are the gradient and intercept of the \log y against \log x graph?
Linear form of y=kb^x?
For y=kb^x, what are the gradient and intercept of the \log y against x graph?
How do you get a from an intercept of \log{10}a=0.477?
Does correlation imply causation?
Describe the correlation as 'strong negative'. What does it mean?
What should you do if a scatter diagram has distinct sections?

Exam questions on Bivariate data, correlation and regression

A study of children aged from 5 to 12 years finds that the regression line of height $h$ cm on age $a$ years is $h=75+5.2a$ .
Use the model to predict the height of a 30-year-old, and comment on the reliability of this prediction.2 marks
A scientist believes that two variables are related by $y=ax^n$ . She plots $\log_{10}y$ against $\log_{10}x$ and finds that the points lie close to a straight line with gradient 1.5 that crosses the vertical axis at 0.477.
Use the model to estimate $y$ when $x=100$ .2 marks
The number $N$ of bacteria, in thousands, in a culture $t$ hours after the start of an experiment is modelled by $N=kb^t$ . A graph of $\log_{10}N$ against $t$ is a straight line passing through the points $(0,\,1.20)$ and $(4,\,2.00)$ .
Show that $\log_{10}N=\log_{10}k+t\log_{10}b$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).