1. 1
   A dealer records the age, $x$ years, and the selling price, $y$ dollars, of 20 used cars of the same model, aged between 1 and 8 years. The regression line of $y$ on $x$ is $y = -1850x + 21400$. The mean age of the 20 cars is 4.2 years.

   (a)

   Use the regression line to estimate the selling price of a 5-year-old car.

   [1 mark]

   • A$\$19\,550$
   • B$\$30\,650$
   • C$\$12\,150$
   • D$\$9250$

   (b)

   Which statement is the correct interpretation of the value $-1850$ in the regression equation?

   [1 mark]

   • AA new car of this model costs about $\$1850$.
   • BThe selling price falls by about $\$1850$ for each additional year of age.
   • CThe selling price falls by a total of $\$1850$ between ages 1 and 8 years.
   • DThe selling price rises by about $\$1850$ for each additional year of age.

   (c)

   Find the mean selling price of the 20 cars.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A teacher records the number of hours, $x$, that each of 12 students spent revising and their test score, $y$, out of 100. The numbers of hours range from 2 to 12. Pearson's product-moment correlation coefficient is $r = 0.81$ and the regression line of $y$ on $x$ is $y = 4.6x + 38.2$.

   (a)

   Estimate the test score of a student who revised for 8 hours.

   [1 mark]

   • A$42.8$
   • B$46.2$
   • C$1.4$
   • D$75.0$

   (b)

   Which of these uses of the regression line is the most reliable?

   [1 mark]

   • AEstimating the score of a student who revised for 5 hours
   • BEstimating the score of a student who revised for 20 hours
   • CEstimating the hours revised by a student who scored 60, by rearranging the equation
   • DEstimating the score of a student who revised for half an hour

   (c)

   The teacher concludes that the data prove that revising for longer causes students to score higher. Comment on this conclusion.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A kiosk records the maximum daily temperature, $x\,^{\circ}\mathrm{C}$, and the number of ice creams sold, $y$, on eight days. The pairs $(x, y)$ are $(18, 72)$, $(21, 88)$, $(23, 93)$, $(25, 104)$, $(26, 106)$, $(28, 121)$, $(30, 127)$, $(33, 142)$. A calculator may be used in this question.

   (a)

   Find the value of Pearson's product-moment correlation coefficient, $r$, and describe the correlation between temperature and ice cream sales.

   [3 marks]

   (b)

   Write down the equation of the regression line of $y$ on $x$. Hence estimate the number of ice creams sold on a day when the maximum temperature is $27\,^{\circ}\mathrm{C}$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An estate agent records the distance, $x$ km, from the city centre and the monthly rent, $y$ dollars, of ten similar flats. The pairs $(x, y)$ are $(1.2, 2150)$, $(2.0, 2010)$, $(2.8, 1890)$, $(3.5, 1820)$, $(4.1, 1700)$, $(5.0, 1650)$, $(6.2, 1480)$, $(7.0, 1450)$, $(8.5, 1300)$, $(9.4, 1260)$. A calculator may be used in this question.

   (a)

   (i) Find the value of $r$ and describe the correlation.
   (ii) Find the equation of the regression line of $y$ on $x$.
   (iii) Interpret, in context, the gradient and the $y$-intercept of your line.

   [6 marks]

   (b)

   (i) Use your line to estimate the monthly rent of a flat 4.5 km from the city centre, and justify that this estimate is reliable.
   (ii) The agent uses the line to estimate the monthly rent of a flat 15 km from the city centre. Find the value he obtains and comment on its reliability.
   (iii) A flat rents for $\$1600$ a month. The agent rearranges the equation of the line to estimate its distance from the city centre. Explain why this is not appropriate.

   [6 marks]

   Total for question 4: 12 marks

End of questions