A collector tracks the value of a vintage guitar over 10 years. The time, $x$ (years), and the value, $y$ (in £1000s), are recorded in the table below.


$x$	1	2	3	4	5	6	7	8	9	10
$y$	8.5	10.2	12.8	15.5	18.9	23.1	28.4	34.2	41.5	50.8

The data is coded using the changes of variable $r = x$ and $s = \log_{10} y$ .

The product moment correlation coefficient for the coded data is 0.97. Comment on $r\,$ for this model and therefore justify the use of a model in the form $y = ab^x$ where $a\,$ and $b\,$ are constants.

The regression line of $s\,$ on $r\,$ is found to be $s = 0.840 + 0.086 r$ .

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

A collector tracks the value of a vintage guitar over 10 years. The time, $x$ (years), and the value, $y$ (in £1000s), are recorded in the table below.


$x$	1	2	3	4	5	6	7	8	9	10
$y$	8.5	10.2	12.8	15.5	18.9	23.1	28.4	34.2	41.5	50.8

The data is coded using the changes of variable $r = x$ and $s = \log_{10} y$ .

The regression line of $s\,$ on $r\,$ is found to be $s = 0.840 + 0.086 r$ .

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

1 Unit 1: Pure Mathematics A

Question 23

Markscheme

1 Unit 1: Pure Mathematics A

Question 23

Markscheme

1 Unit 1: Pure Mathematics A

Question 23

1 Unit 1: Pure Mathematics A Questions

1 Unit 1: Pure Mathematics A

Question 23

1 Unit 1: Pure Mathematics A Questions