2017 H2 Mathematics Paper 2 Question 8

Linear Correlation and Regression

Answers

(a)

(i)
(ii)
(iii)
(bi)
(D) y=ax+b{y=a\sqrt{x}+b}
(bii)
y=74.0+4.18x{y = 74.0+4.18\sqrt{x}}
r=0.981{r=0.981}
(biii)
  • x=189{x=189} lies within the given data range 0≤x≤200.{0\leq x \leq 200.}
  • ∣r∣≈1{|r|\approx 1} which suggest a strong linear correlation between x{\sqrt{x}} and y.{y.}

Full solutions

(a)

(i)
(ii)
(iii)
(bi)
y=ax+b\begin{equation} \qquad y=a\sqrt{x}+b \tag{D} \end{equation}
(bii)
y=74.0+4.18x (3 sf)  ■r=0.981 (3 sf)  ■\begin{gather*} y = 74.0+4.18\sqrt{x} \textrm{ (3 sf)} \; \blacksquare \\ r = 0.981 \textrm{ (3 sf)} \; \blacksquare \end{gather*}
(biii)
  • x=189{x=189} lies within the given data range 0≤x≤200.  ■{0\leq x \leq 200. \; \blacksquare}
  • ∣r∣≈1{|r|\approx 1} which suggest a strong linear correlation between x{\sqrt{x}} and y.  ■{y. \; \blacksquare}