Specimen 2017 H2 Mathematics Paper 2 Question 6

Linear Correlation and Regression

Answers

{d}

increases,

{m}

increases at an increasing rate so they should not be modelled by a linear equation

{y=ax+b.}

For

{m=ed^2 + f,}

{r=0.98889.}

For

{m=gd^3+h,}

{r=0.99951.}

Since the

{|r|\textrm{-value}}

is closer to

{1,}

{m=gd^3+h}

is the better model.

Least square regression line of ${m}$ on ${d^3:}$ ${m = 3.74+0.572d^3.}$

{127 \textrm{ kg}.}

{992 \textrm{ kg}.}

The answer for (a) is more reliable as the top length of

{6 \textrm{ m}}

lies within the given data range

{2.31 \leq d \leq 9.17}

while the top length of

{12 \textrm{ m}}

lies outside the given data range.

{d}

increases,

{m}

increases at an increasing rate so they should not be modeled by a linear equation

{y=ax+b \; \blacksquare}

For

{m=ed^2 + f,}

{r=0.98889.}

For

{m=gd^3+h,}

{r=0.99951.}

Since the ${|r|\textrm{-value}}$ is closer to ${1,}$ the better model is ${m=gd^3+h \; \blacksquare}$

Least square regression line of ${m}$ on ${d^3:}$

m = 3.74+0.572d^3 \; \blacksquare

(iiia)

\begin{align*} m &= 0.57165(6)^3 + 3.7431 \\ &= 127 \textrm{ (3 sf) kg} \; \blacksquare \end{align*}

(iiib)

\begin{align*} m &= 0.57165(12)^3 + 3.7431 \\ &= 992 \textrm{ (3 sf) kg} \; \blacksquare \end{align*}

The answer for (a) is more reliable as the top length of

{6 \textrm{ m}}

lies within the given data range

{2.31 \leq d \leq 9.17}

while the top length of

{12 \textrm{ m}}

lies outside the given data range.