1. 1
   A researcher records the number of hours studied (x) and the exam score (%, y) for 8 students: (1, 45), (2, 50), (3, 60), (4, 65), (5, 72), (6, 78), (7, 85), (8, 90).

   (a)

   What type of correlation does this data show?

   [1 mark]

   • APositive correlation
   • BNegative correlation
   • CZero correlation
   • DNo pattern

   (b)

   As the number of hours studied increases, what generally happens to the exam score?

   [1 mark]

   • AIt generally decreases
   • BIt generally increases
   • CIt stays exactly the same
   • DIt varies randomly with no pattern

   (c)

   Using the trend in the data, which of the following is the best estimate of the exam score for a student who studies 4.5 hours?

   [1 mark]

   • A60
   • B55
   • C75
   • D68

   Total for question 1: 3 marks

2. 2
   A gardener records the amount of fertiliser (g), x, given to 6 plants and their height (cm), y, after a month: (10, 18), (20, 24), (30, 30), (40, 35), (50, 41), (60, 48).

   (a)

   Describe the type and strength of correlation shown by this data.

   [2 marks]

   (b)

   Using the trend in the data, estimate the height of a plant given 35 g of fertiliser.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A line of best fit for a scatter graph relating advertising spend (£1000s), x, and monthly sales (£1000s), y, passes through the points (2, 15) and (8, 45).

   (a)

   Find the gradient of the line of best fit.

   [3 marks]

   (b)

   Find the equation of the line of best fit in the form $y = mx + c$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A scientist studies the relationship between temperature (°C), x, and the number of ice creams sold, y, at a beach kiosk over 10 days, and finds a positive correlation. The line of best fit passes through the points (18, 40) and (30, 160).

   (a)

   Find the equation of the line of best fit in the form $y = mx + c$.

   [4 marks]

   (b)

   Use the line of best fit to estimate the number of ice creams sold when the temperature is 25°C.

   [4 marks]

   (c)

   The scientist wants to use the line of best fit to predict sales when the temperature is 40°C. State the predicted value, and explain why this prediction may be unreliable.

   [5 marks]

   Total for question 4: 13 marks

End of questions