IB Maths AA SL AA 4.2 Correlation and regression questions

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Question 1

Paper 1, no calculatorEasy6 marks

A student records the average daily sunlight exposure, $x$ hours, and the height after four weeks, $y$ cm, of five seedlings of the same species.

$x$	2	3	4	5	6
$y$	11	12	17	17	18

For these data, the Pearson correlation coefficient is $r=0.93$ and the regression line of $y$ on $x$ is $y=1.9x+7.4$

(a)

State the strength and direction of the correlation. State whether this result alone shows that sunlight causes greater height.

[2]

(b)

Use the regression line to estimate the height of a seedling receiving 5 hours of sunlight per day.

[2]

(c)

Interpret the gradient of the regression line in this context.

[1]

(d)

The observed sunlight exposures range from 2 to 6 hours per day. Explain why using the regression line to estimate the height at 10 hours per day may be unreliable.

[1]

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