| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2019 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate y on x from summary statistics |
| Difficulty | Moderate -0.3 This is a straightforward application of standard regression formulas given all necessary summary statistics. Part (i) requires the formula b = r(sy/sx) and substitution into y = a + bx. Part (ii) is a routine hypothesis test for correlation with given critical values. Part (iii) is simple substitution. All steps are mechanical with no problem-solving or insight required, making it slightly easier than average. |
| Spec | 5.08d Hypothesis test: Pearson correlation5.09c Calculate regression line5.09e Use regression: for estimation in context |
| Mean | Variance | |
| \(x\) | 3.3125 | 3.3086 |
| \(y\) | 6.7375 | 7.9473 |
10 The means and variances for a random sample of 8 pairs of values of $x$ and $y$ taken from a bivariate distribution are given in the following table.
\begin{center}
\begin{tabular}{ | c | c | c | }
\hline
& Mean & Variance \\
\hline
$x$ & 3.3125 & 3.3086 \\
\hline
$y$ & 6.7375 & 7.9473 \\
\hline
\end{tabular}
\end{center}
The product moment correlation coefficient for the sample is 0.5815 , correct to 4 decimal places.\\
(i) Find the equation of the regression line of $y$ on $x$.\\
(ii) Test at the $5 \%$ significance level whether there is evidence of positive correlation between $x$ and $y$. [4]\\
(iii) Calculate an estimate of $y$ when $x = 6.0$ and comment on the reliability of your estimate.\\
\hfill \mbox{\textit{CAIE FP2 2019 Q10 [12]}}