Correlation and regressionIB MYP Maths Extended: Mind map

Exam questions on Correlation and regression

1. A researcher in Toronto collects data from 40 teenagers and finds that the correlation coefficient $r$ between their daily screen time (hours) and their sleep (hours) is $r=-0.82$.
   The researcher also finds $r=0.1$ between screen time and test scores. Describe this correlation and say what its scatter graph would look like.2 marks
2. A student uses technology to investigate four sets of data. Set 1: line of best fit $y=2x+3$, points close to the line, $r=0.96$. Set 2: line of best fit $y=-0.5x+10$, points close to the line, $r=-0.93$. Set 3: line of best fit $y=0.3x+1$, points widely scattered about the line, $r=0.28$. Set 4: line of best fit $y=-4x+7$, points widely scattered about the line, $r=-0.31$.
   A sixth set has line of best fit $y=-3x+20$ and the points are widely scattered about the line. Use the pattern to describe its correlation.2 marks
3. A kiosk in Mumbai records the maximum daily temperature $T$ ($^\circ$C) and the number $n$ of cold drinks sold on six days. The data are: $(24,31)$, $(27,38)$, $(29,41)$, $(31,52)$, $(33,57)$, $(36,66)$. Use technology.
   Find the equation of the line of best fit for $n$ against $T$, and the value of $r$. Describe the correlation.3 marks