CIMA BA1 · Chapter 11

Forecasting: correlation, regression and time series MCQs with Answers

11 multiple-choice questions on Forecasting: correlation, regression and time series for CIMA BA1 Fundamentals of Business Economics. Try each one before revealing the answer and explanation.

1. Question 1

   A correlation coefficient of -0.9 between two variables indicates:

   • A) A weak negative linear relationship
   • B) A strong negative linear relationship
   • C) A strong positive linear relationship
   • D) That 90% of the change in one variable is caused by the other
   Show answer & explanation

   Answer: B) A strong negative linear relationship

   The correlation coefficient lies between -1 and +1. A value close to -1 indicates a strong linear relationship where one variable tends to fall as the other rises. Correlation does not prove causation.

2. Question 2

   The correlation coefficient between advertising spend and sales is 0.8. What proportion of the variation in sales is explained by the variation in advertising spend?

   • A) 64%
   • B) 80%
   • C) 89%
   • D) 36%
   Show answer & explanation

   Answer: A) 64%

   The coefficient of determination is r squared = 0.8 x 0.8 = 0.64. So 64% of the variation in sales is explained by the variation in advertising; the remaining 36% is due to other factors.

3. Question 3

   Five pairs of observations give: sum of x = 15, sum of y = 27, sum of xy = 93, sum of x squared = 55, n = 5. What is the least squares regression line of y on x?

   • A) y = 1.2 + 1.8x
   • B) y = 5.4 + 1.2x
   • C) y = 1.8 + 0.22x
   • D) y = 1.8 + 1.2x
   Show answer & explanation

   Answer: D) y = 1.8 + 1.2x

   b = (n x sum xy - sum x x sum y) / (n x sum x squared - (sum x) squared) = (5 x 93 - 15 x 27) / (5 x 55 - 15 x 15) = (465 - 405) / (275 - 225) = 60 / 50 = 1.2. a = mean of y - b x mean of x = 27/5 - 1.2 x 15/5 = 5.4 - 3.6 = 1.8. So y = 1.8 + 1.2x.

4. Question 4

   A company's monthly sales (units) are forecast using the trend equation y = 1,200 + 35x, where x is the month number. What is the trend forecast for month 24?

   • A) 28,835 units
   • B) 1,235 units
   • C) 2,040 units
   • D) 2,075 units
   Show answer & explanation

   Answer: C) 2,040 units

   Substitute x = 24: y = 1,200 + 35 x 24 = 1,200 + 840 = 2,040 units.

5. Question 5

   Two judges rank six products. The sum of the squared differences between their ranks is 10. What is Spearman's rank correlation coefficient (to three decimal places)?

   • A) 0.286
   • B) 0.714
   • C) 0.952
   • D) -0.714
   Show answer & explanation

   Answer: B) 0.714

   R = 1 - (6 x sum d squared) / (n(n squared - 1)) = 1 - (6 x 10) / (6 x 35) = 1 - 60 / 210 = 0.714. This indicates fairly strong agreement between the judges.

6. Question 6

   Why are forecasts produced by extrapolation from a regression line generally less reliable than those produced by interpolation?

   • A) Extrapolation assumes the relationship continues outside the range of observed data, which may not hold
   • B) Extrapolation uses a lower correlation coefficient
   • C) Interpolation always uses more data points than extrapolation
   • D) Extrapolation can only be used with time series data
   Show answer & explanation

   Answer: A) Extrapolation assumes the relationship continues outside the range of observed data, which may not hold

   Interpolation estimates values within the range of the data used to calculate the regression line. Extrapolation goes beyond that range, assuming the same linear relationship holds where it has not been observed, so the forecast is less reliable.

7. Question 7

   Which of the following is NOT one of the components normally identified in a time series analysis?

   • A) Trend
   • B) Seasonal variation
   • C) Random (residual) variation
   • D) Correlation component
   Show answer & explanation

   Answer: D) Correlation component

   A time series is normally analysed into the trend, seasonal variations, cyclical variations and random (residual) variations. Correlation is a measure of association between two variables, not a component of a time series.

8. Question 8

   Using an additive time series model, the trend value for a quarter is 820 units and the seasonal variation for that quarter is +35 units. What is the forecast for the quarter?

   • A) 785 units
   • B) 820 units
   • C) 855 units
   • D) 28,700 units
   Show answer & explanation

   Answer: C) 855 units

   In the additive model, forecast = trend + seasonal variation = 820 + 35 = 855 units.

9. Question 9

   Using a multiplicative time series model, the trend value for a quarter is 1,250 units and the seasonal index is 1.12. What is the forecast for the quarter?

   • A) 1,116 units
   • B) 1,400 units
   • C) 1,100 units
   • D) 1,362 units
   Show answer & explanation

   Answer: B) 1,400 units

   In the multiplicative model, forecast = trend x seasonal index = 1,250 x 1.12 = 1,400 units.

10. Question 10

    Actual sales in Quarter 3 were 2,310 units. Using a multiplicative model, the seasonal index for Quarter 3 is 1.10. What are the seasonally adjusted (deseasonalised) sales for the quarter?

    • A) 2,100 units
    • B) 2,541 units
    • C) 2,079 units
    • D) 2,520 units
    Show answer & explanation

    Answer: A) 2,100 units

    Seasonally adjusted figure = actual / seasonal index = 2,310 / 1.10 = 2,100 units. Removing the seasonal effect shows the underlying level of sales; multiplying by the index would add the seasonal effect again.

11. Question 11

    Sales for five consecutive periods were 40, 46, 52, 49 and 55. What is the three-period moving average centred on period 3?

    • A) 46
    • B) 52
    • C) 48.4
    • D) 49
    Show answer & explanation

    Answer: D) 49

    The three-period moving average centred on period 3 uses periods 2, 3 and 4: (46 + 52 + 49) / 3 = 147 / 3 = 49.