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1.6.8 Reduction to linear form

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Question 7

An urban planner monitors the population growth of a developing city over 10 decades. The number of decades, $x$ , and the population in thousands, $y$ , are recorded in the table below.


$x$	1	2	3	4	5	6	7	8	9	10
$y$	18	26	38	55	78	112	158	225	321	460

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 0.998. 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.

[3]

The regression line of $s\,$ on $r\,$ is found to be $s = 1.12 + 0.155 r$ .

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

[3]

Markscheme

1.6.8 Reduction to linear form Questions

A Level
Maths
1.6.8 Reduction to linear form

42 exam-style questions on OCR A Level Maths 1.6.8 Reduction to linear form. Each one has a worked solution and a mark scheme showing where the marks go.

1.6.8 Reduction to linear form

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1.6.8 Reduction to linear form

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Question 7

An urban planner monitors the population growth of a developing city over 10 decades. The number of decades, $x$ , and the population in thousands, $y$ , are recorded in the table below.


$x$	1	2	3	4	5	6	7	8	9	10
$y$	18	26	38	55	78	112	158	225	321	460

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

[3]

The regression line of $s\,$ on $r\,$ is found to be $s = 1.12 + 0.155 r$ .

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

[3]

Markscheme

1.6.8 Reduction to linear form Questions

A Level
Maths
1.6.8 Reduction to linear form

42 exam-style questions on OCR A Level Maths 1.6.8 Reduction to linear form. Each one has a worked solution and a mark scheme showing where the marks go.