Product moment correlation coefficientEdexcel International A Level Maths: Mind map

Exam questions on Product moment correlation coefficient

1. A dealer records the age, $x$ years, and the value, $y$ thousand pounds, of 10 used cars of the same model. The summary statistics are $S_{xx}=40$, $S_{yy}=90$ and $S_{xy}=-48$.
   The dealer converts the ages into months and the values into pounds. State the new value of $r$ and justify your answer.2 marks
2. A seaside town records, for each of 12 months, the ice cream sales, $x$ hundred cones, and the number of sunburn cases, $y$, treated at the local clinic. The product moment correlation coefficient for these data is $r=0.91$.
   Suggest a reason why the two variables are strongly correlated, even though neither is likely to cause the other.2 marks
3. A teacher records the number of practice tests, $x$, completed by five students and their scores, $y$, out of 5 in a final quiz. The values of $x$ are 1, 2, 3, 4, 5 and the scores are 2, 4, 5, 4, 5. For these data $\sum x=15$, $\sum y=20$, $\sum x^2=55$, $\sum y^2=86$ and $\sum xy=66$.
   Find $S_{xx}$, $S_{yy}$ and $S_{xy}$.3 marks