2014 H2 Mathematics Paper 2 Question 8

Linear Correlation and Regression

Answers

(A)

{r=-0.947}

(B)

{r=-0.975}

{P = c \ln m + d}

is the better model as the product moment correlation coefficient is closer to

{-1, }

indicating a stronger linear correlation

P = -33,700 \ln m + 196,000

Price

{=\$64,000}

(ai)

(aii)

(bi)

(A) Using a GC, product moment correlation coefficient between

{m}

and

{P:}

r_1 = -0.947 \textrm{ (3 sf)} \; \blacksquare

(B) Product moment correlation coefficient between

{\ln m}

and

{P:}

r_2 = -0.975 \textrm{ (3 sf)} \; \blacksquare

(bii)

{P = c \ln m + d}

is the better model as the product moment correlation coefficient is closer to

{-1, }

indicating a stronger linear correlation

{\blacksquare}

Least square regression line of

{P}

{\ln m:}

\begin{align*} & P = -33,660 \ln m + 195,694 \\ & P = -33,700 \ln m + 196,000 \textrm{ (3 sf)} \; \blacksquare \end{align*}

(biii)

When

{m=50,}

\begin{align*} & \textrm{Estimated price} \\ &= -33,660 \ln 50 + 195,694 \\ &= \$64,000 \textrm{ (3 sf)} \; \blacksquare \end{align*}