Scatter diagrams and linear regressionEdexcel International A Level Maths: Mind map

Exam questions on Scatter diagrams and linear regression

1. A teacher records the number of hours of revision per week, $x$, and the mark out of 40, $y$, in a test for 8 students. The summary statistics are $\bar{x}=5$, $\bar{y}=22$, $S_{xx}=40$ and $S_{xy}=62$. The regression line of $y$ on $x$ is $y=a+bx$.
   Estimate the mark of a student who revises for 6 hours per week.2 marks
2. A cafe owner models the daily sales, $s$ pounds, against the midday temperature, $t$ °C, using the regression line $s=120+8.5t$. The model was fitted to data collected on days when the temperature was between 12 °C and 28 °C.
   A student uses the model to predict the sales on a day when the midday temperature is 5 °C. Explain why this prediction may be unreliable.2 marks
3. A gardener applies $x$ grams of fertiliser to each of five plants of the same type and measures the height, $y$ cm, of each plant after four weeks. The values of $x$ are 2, 4, 6, 8, 10 and the heights are 5, 9, 10, 15, 16. For these data $\sum x=30$, $\sum y=55$, $\sum x^2=220$ and $\sum xy=386$.
   Find the values of $S_{xx}$ and $S_{xy}$.3 marks