Correlation and regressionIB MYP Maths Extended: Subtopic test

1. 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 $r=-0.82$.

   (a)

   Which description of the correlation is correct?

   [1 mark]

   • Astrong negative correlation
   • Bweak negative correlation
   • Cstrong positive correlation
   • Dno correlation

   (b)

   Which conclusion is supported by the data?

   [1 mark]

   • AMore screen time causes teenagers to sleep less
   • B$82\%$ of teenagers who use screens sleep less
   • CThere is no relationship between screen time and sleep
   • DTeenagers with more screen time tend to sleep fewer hours

   (c)

   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]

   Total for question 1: 4 marks

2. 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)

   A fifth set has line of best fit $y=-0.2x+8$ and the points are very close to the line. Which value of $r$ is most likely?

   [1 mark]

   • A$-0.2$
   • B$-0.97$
   • C$0.97$
   • D$0.2$

   (b)

   Which statement describes the pattern in the four sets?

   [1 mark]

   • AA steeper gradient always gives $r$ closer to $1$ or $-1$
   • BThe sign of $r$ is the opposite of the sign of the gradient
   • CThe sign of $r$ matches the sign of the gradient, and the closeness of $r$ to $1$ or $-1$ depends on how close the points are to the line
   • DThe value of $r$ equals the gradient

   (c)

   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]

   Total for question 2: 4 marks

3. 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.

   (a)

   Find the equation of the line of best fit for $n$ against $T$, and the value of $r$. Describe the correlation.

   [3 marks]

   (b)

   Use your equation to predict the number of drinks sold when $T=30$ and when $T=45$. Comment on the reliability of each prediction.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A dealer in Dubai records the age $a$ (years) and the price $p$ (thousand AED) of eight used cars of the same model. The data are: $(1,62)$, $(2,55)$, $(3,49)$, $(4,41)$, $(5,38)$, $(6,30)$, $(7,27)$, $(8,19)$. Use technology.

   (a)

   (i) Find the value of $r$ and describe the correlation.
   (ii) Find the equation of the line of best fit for $p$ against $a$.
   (iii) Interpret the gradient in this context.
   (iv) Estimate the price of a car that is $5.5$ years old.

   [6 marks]

   (b)

   The dealer uses the line to set the price of a 12-year-old car. Evaluate how reliable this is, and explain what the dealer should do.

   [6 marks]

   Total for question 4: 12 marks

End of questions