IB Maths AI SL 4.4 Correlation and regression Question Bank

Practise IB Mathematics SL/HL 4.4 by applying correlation and regression methods to exam-style questions.

[Maximum number: 8]

The mean annual temperatures for Earth, recorded at fifty-year intervals, are shown in the table.

Table for Question SL 4.4—Correlation and regression question 1 — IB Maths AI SL

Tami creates a linear model for this data by finding the equation of the straight line passing through the points with coordinates (1708,8.73) and (1958,9.45).

(a)

Find the equation of the regression line y on x.

[ 3 ]

$y=0.00256 x+4.46(0.00255714 \ldots x+4.46454 \ldots)$
(M1)A1

Note: Award (M1)A0 for answers that show the correct method, but are presented incorrectly (e.g. no " y= " or truncated values etc.). Accept 4.465 as the correct answer to 4 sf .

(b)

Find the value of r, the Pearson's product-moment correlation coefficient.

[ 3 ]

(c)

Use Thandizo's model to estimate the mean annual temperature in the year 2000.

Thandizo uses his regression line to predict the year when the mean annual temperature will first exceed $15^{\circ} \mathrm{C}$ .

[ 2 ]

attempt to substitute 2000 into their part (e)(i)
$0.00255714 \ldots \times 2000+4.46454 \ldots$ $=9.58\left({ }^{\circ} \mathrm{C}\right)\left(9.57882 \ldots\left({ }^{\circ} \mathrm{C}\right)\right)$

Note: Award A1 for 9.57 from $0.00255714 \times 2000+4.46$ .

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SL 4.4—Correlation and regression question 1

Question (a)

Question (b)

Question (c)