Bivariate data, correlation and regressionEdexcel A-Level Maths: Mind map

Exam questions on Bivariate data, correlation and regression

1. 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
2. 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
3. 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