As part of a statistics project, Gill collected data relating to the length of time, to the nearest minute, spent by shoppers in a supermarket and the amount of money they spent. Her data for a random sample of 10 shoppers are summarised in the table below, where $t\,$ represents time and $\pounds m\,$ the amount spent over £20.

$t$ (minutes)	$£m\pounds m$
15	-3
23	17
5	-19
16	4
30	12
6	-9
32	27
23	6
35	20
27	6

Write down the actual amount spent by the shopper who was in the supermarket for 15 minutes.

Calculate $S_{tt}$ , $S_{mm}$ and $S_{tm}$ .

(You may use $∑t2=5478\sum t^2 = 5478$ , $∑m2=2101\sum m^2 = 2101$ , and $∑tm=2485\sum tm = 2485$ )

Calculate the value of the product moment correlation coefficient between $t\,$ and $m$ .

Write down the value of the product moment correlation coefficient between $t\,$ and the actual amount spent. Give a reason to justify your value.

Give an interpretation to both of these coefficients (0.914 and 0.178).

Suggest a practical reason why these two values are so different.

$t$ (minutes)	$£m\pounds m$
15	-3
23	17
5	-19
16	4
30	12
6	-9
32	27
23	6
35	20
27	6

Write down the actual amount spent by the shopper who was in the supermarket for 15 minutes.

Calculate $S_{tt}$ , $S_{mm}$ and $S_{tm}$ .

(You may use $∑t2=5478\sum t^2 = 5478$ , $∑m2=2101\sum m^2 = 2101$ , and $∑tm=2485\sum tm = 2485$ )

Calculate the value of the product moment correlation coefficient between $t\,$ and $m$ .

Write down the value of the product moment correlation coefficient between $t\,$ and the actual amount spent. Give a reason to justify your value.

Give an interpretation to both of these coefficients (0.914 and 0.178).

Suggest a practical reason why these two values are so different.

Correlation and Regression

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Markscheme

Correlation and Regression

Question 2

Markscheme

Correlation and Regression

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Correlation and Regression Questions

Correlation and Regression

Question 2

Correlation and Regression Questions