The variables $x\,$ and $y\,$ are recorded on 10 occasions. The data are coded using the changes of variable $r = x$ and $s = \log_{10} y$ .

The product moment correlation coefficient between $r\,$ and $s\,$ is 0.98, and the regression line of $s\,$ on $r\,$ is

$s = 2.60 + 0.127 r$

Explain how the value 0.98 justifies using a model of the form $y = ab^{x}$ , where $a\,$ and $b\,$ are constants.

Find the value of $a\,$ and the value of $b$ . Give your answers to 3 significant figures.

The variables $x\,$ and $y\,$ are recorded on 10 occasions. The data are coded using the changes of variable $r = x$ and $s = \log_{10} y$ .

The product moment correlation coefficient between $r\,$ and $s\,$ is 0.98, and the regression line of $s\,$ on $r\,$ is

$s = 2.60 + 0.127 r$

Explain how the value 0.98 justifies using a model of the form $y = ab^{x}$ , where $a\,$ and $b\,$ are constants.

Find the value of $a\,$ and the value of $b$ . Give your answers to 3 significant figures.

2.2.2 Scatter diagrams and correlation

2.2.2 Scatter diagrams and correlation Questions