4.4 Correlation and linear regressionIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 4.4 Correlation and linear regression

1. Over eight days a café records the maximum daily temperature, $T\,^\circ$C, and the number of cold drinks sold, $n$. $T$: 18, 21, 24, 26, 29, 31, 34, 36. $n$: 42, 55, 61, 70, 82, 85, 96, 104. The regression line of $n$ on $T$ has equation $n=aT+b$. Use your GDC.
   Use your regression line to estimate the number of cold drinks sold on a day when the maximum temperature is $28\,^\circ$C.2 marks
2. Over 12 months, a coastal town records its monthly ice-cream sales and the number of sunburn cases treated at its clinic. Pearson's product-moment correlation coefficient for the data is $r=0.91$.
   Suggest a third variable that could explain the correlation between ice-cream sales and sunburn cases.2 marks
3. A teacher records the number of hours, $x$, that eight students revised for a test and their test score, $y$ (out of 100). $x$: 2, 4, 5, 6, 8, 9, 10, 12. $y$: 45, 52, 50, 61, 63, 70, 66, 78. Use your GDC.
   Find the value of Pearson's product-moment correlation coefficient $r$, and the equation of the regression line of $y$ on $x$.3 marks