2015 H2 Mathematics Paper 2 Question 10

Linear Correlation and Regression

Answers

{-0.9807}

{-0.9748}

{-0.9986}

{P = 34.8-0.147\sqrt{h}}

{P = 34.8-0.266\sqrt{H}}

(iia)

Product moment correlation coefficient between

{h}

and

{P:}

r_1 = -0.9807 \textrm{ (4 dp)} \; \blacksquare

(iib)

Product moment correlation coefficient between

{\ln h}

and

{P:}

r_2 = -0.9748 \textrm{ (4 dp)} \; \blacksquare

(iic)

Product moment correlation coefficient between

{\sqrt{h}}

and

{P:}

r_3 = -0.9986 \textrm{ (4 dp)} \; \blacksquare

Equation of least square regression line of

{P}

{\sqrt{h}:}

\begin{align*} & P = 34.789-0.14687\sqrt{h} \\ & P = 34.8-0.147\sqrt{h} \textrm{ (3 sf)} \; \blacksquare \end{align*}

Let

{H}

denote the height above sea-level, measured in metres

\begin{align*} 1 \textrm{ metre} &= 3.28 \textrm{ feet} \\ H \textrm{ metre} &= 3.28H \textrm{ feet} \\ h &= 3.28H \end{align*}

\begin{align*} & P = 34.789-0.14687\sqrt{h} \\ & P = 34.789 - 0.14687 \sqrt{3.28H} \\ & P = 34.8-0.266\sqrt{H} \textrm{ (3 sf)} \; \blacksquare \end{align*}