1. 1
   A beach kiosk records, on a number of summer days, the hours of sunshine, $x$, and the number of ice creams sold, $y$. The regression line of $y$ on $x$ is $y=2x+10$ and the regression line of $x$ on $y$ is $x=0.4y-2$.

   (a)

   Find the mean point $(\bar{x},\bar{y})$ of the data.

   [1 mark]

   • A$(10,\,30)$
   • B$(30,\,10)$
   • C$(-2,\,10)$
   • D$(-5,\,0)$

   (b)

   Estimate the number of ice creams sold on a day with 12 hours of sunshine.

   [1 mark]

   • A$35$
   • B$34$
   • C$2.8$
   • D$24$

   (c)

   On one day the kiosk sold 36 ice creams. Estimate the number of hours of sunshine on that day.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Eight students record the number of hours they slept, $x$, the night before a test of their reaction time, $y$ milliseconds. The data are:
   $x$: 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0, 9.0
   $y$: 305, 290, 300, 272, 285, 262, 270, 248
   (in the same order, so the first student slept 5.0 hours and had a reaction time of 305 ms). A calculator may be used in this question.

   (a)

   Find the equation of the regression line of $x$ on $y$, with coefficients correct to 3 significant figures.

   [1 mark]

   • A$x=-0.0753y+27.8$
   • B$y=-13.3x+369$
   • C$x=-13.3y+369$
   • D$x=-0.0624y+24.2$

   (b)

   Another student had a reaction time of 290 ms. Find the best estimate of the number of hours this student slept.

   [1 mark]

   • A$5.98$
   • B$6.81$
   • C$6.13$
   • D$-3480$

   (c)

   A student's reaction time is 340 ms. The regression line of $x$ on $y$ gives an estimate of 3.0 hours of sleep for this student. Explain why this estimate is not reliable.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A dealer records the age, $x$ years, and the price, $y$ thousand dollars, of seven used cars of the same model. The data are:
   $x$: 1, 2, 3, 4, 6, 7, 9
   $y$: 17.0, 16.5, 13.0, 14.5, 9.0, 11.5, 7.0
   (in the same order). A calculator may be used in this question.

   (a)

   (i) Write down the value of Pearson's product-moment correlation coefficient, $r$.
   (ii) Find the equation of the regression line of $x$ on $y$.

   [3 marks]

   (b)

   A car of this model is advertised for 12.0 thousand dollars, but its age is not stated. Estimate the age of the car. Justify your choice of regression line and comment on the reliability of your estimate.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Five pairs of data $(x,y)$ are $(2,5)$, $(4,9)$, $(6,p)$, $(8,16)$ and $(10,20)$, where $p$ is a constant. The mean of the $y$-values is 12. A calculator may be used in this question.

   (a)

   (i) Find the value of $p$.
   (ii) Write down the value of $r$ and find the equation of the regression line of $x$ on $y$.
   (iii) Verify that the regression line of $x$ on $y$ passes through the mean point $(\bar{x},\bar{y})$.

   [6 marks]

   (b)

   (i) Find the equation of the regression line of $y$ on $x$.
   (ii) Use the appropriate regression line to estimate the value of $x$ when $y=14$, and the value of $y$ when $x=7$.
   (iii) Substituting your estimate of $y$ from part (ii) into the regression line of $x$ on $y$ does not give exactly $x=7$. Explain why.

   [6 marks]

   Total for question 4: 12 marks

End of questions