2010 H2 Mathematics Paper 2 Question 10

Linear Correlation and Regression

Answers

{0.9860}

{0.9907}

{F = c + d v^2}

is a better model.

From part (i), the scatter diagram suggests that, as

{v}

increases,

{F}

increases at an increasing rate, which is more consistent with a quadratic model rather than a linear model.

From part (ii), the product moment correlation coefficient between

{v^2}

and

{F}

is also closer to

{1,}

indicating a stronger linear correlation between

{v^2}

and

{F}

compared to between

{v}

and

{F}

{F = 3.20+0.0242v^2}

{F=30.7}

Neither the regression line of

{v}

{F}

nor the regression line of

{v^2}

{F}

should be used because

{v}

is the independent variable in this scenario.

(iia)

Using a GC, product moment correlation between

{v}

and

{F:}

r_1 = 0.9860 \textrm{ (4 dp)} \; \blacksquare

(iib)

Product moment correlation between

{v^2}

and

{F:}

r_2 = 0.9907 \textrm{ (4 dp)} \; \blacksquare

{F = c + d v^2}