Correlation and regression

Sample questions

Original practice questions written in the style of the exam.

1. Question 17 marks

   A teacher records the number of hours of revision, $x$, and the test score, $y$, for 8 students. The data are summarised by $\sum x = 56,\quad \sum y = 452,\quad \sum x^2 = 484,\quad \sum y^2 = 27\,056,\quad \sum xy = 3535.$

   (a) Find $S_{xx}$, $S_{yy}$ and $S_{xy}$.

   (b) Calculate the product moment correlation coefficient between $x$ and $y$.

   (c) Find the equation of the regression line of $y$ on $x$ in the form $y = a + bx$.

   (d) Estimate the score of a student who revises for 7 hours.

   Mark scheme

   • (a) $S_{xx} = 484 - \dfrac{56^2}{8} = 92$ (1)