1 Five observations of bivariate data \(( x , y )\) are given in the table.
| \(x\) | 7 | 8 | 12 | 6 | 4 |
| \(y\) | 20 | 16 | 7 | 17 | 23 |
- Find the value of Pearson's product-moment correlation coefficient.
- State what your answer to part (a) tells you about a scatter diagram representing the data.
- A new variable \(a\) is defined by \(a = 3 x + 4\). Dee says "The value of Pearson's product-moment correlation coefficient between \(a\) and \(y\) will not be the same as the answer to part (a)."
State with a reason whether you agree with Dee.
An investor obtains data about the profits of 8 randomly chosen investment accounts over two one-year periods.
The profit in the first year for each account is \(p \%\) and the profit in the second year for each account is \(q \%\).
The results are shown in the table and in the scatter diagram.
| Account | A | B | C | D | E | F | G | H |
| \(p\) | 1.6 | 2.1 | 2.4 | 2.7 | 2.8 | 3.3 | 5.2 | 8.4 |
| \(q\) | 1.6 | 2.3 | 2.2 | 2.2 | 3.1 | 2.9 | 7.6 | 4.8 |
\includegraphics[max width=\textwidth, alt={}, center]{4c7546b9-03ee-47a1-915f-41e2b4ca19c0-03_762_1248_906_260} - State which, if either, of the variables \(p\) and \(q\) is independent.
- Calculate the equation of the regression line of \(q\) on \(p\).
- Use the regression line to estimate the value of \(q\) for an investment account for which \(p = 2.5\).
- Give two reasons why this estimate could be considered reliable.
- Comment on the reliability of using the regression line to predict the value of \(q\) when \(p = 7.0\).