- 25 Marks
Question
The Human Resource Manager of a bank was worried about the number of international training programmes attended by the staff every year(x) and the corresponding allowances (GHe y). A random sample of 10 training programmes gave the following results:
| x (days) | 10 | 3 | 8 | 17 | 5 | 9 | 14 | 16 | 21 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|
| Staff Allowance(y) (GHe) | 116 | 39 | 85 | 159 | 61 | 94 | 143 | 178 | 225 | 134 |
(a) Find an equation of the regression line of Y on X in the form Y = a + bX. (10 marks)
(b) Interpret the slope b and intercept a of your line. (5 marks)
(c) Find the expected allowance to be paid for a training programme that lasted for 11 days. (5 marks)
(d) State and give a reason, whether or not you would use the line to find the expected training lasting for 2 months. (5 marks)
Answer
a) The least squares regression line is found using:
b (slope) = [n × Σ(xy) – Σx × Σy] / [n × Σ(x²) – (Σx)²]
a (intercept) = [Σy – b × Σx] / n
Given data:
Σx = 116, Σy = 1234, Σxy = 17128, Σx² = 1630, n = 10
b = [10 × 17128 – 116 × 1234] / [10 × 1630 – 116²] = [171280 – 143144] / [16300 – 13456] = 28136 / 2844 ≈ 9.89
a = [1234 – 9.89 × 116] / 10 ≈ [1234 – 1147.24] / 10 = 86.76 / 10 ≈ 8.68
Thus, Y = 8.68 + 9.89X (rounded to two decimals; exact calculations may vary slightly based on precision).
In Ghanaian banks like Stanbic Bank Ghana, such regression aids HR in budgeting allowances, ensuring compliance with labor laws and internal governance.
b) The slope b ≈ 9.89 indicates that for each additional day of training, the allowance increases by approximately GHe9.89, reflecting per diem or related costs.
The intercept a ≈ 8.68 represents the fixed allowance when training days are zero, possibly base administrative costs, though practically, zero-day training is unlikely.
This interpretation helps in cost forecasting, aligning with BoG’s operational risk standards under Basel II.
c) For X = 11: Y = 8.68 + 9.89 × 11 ≈ 8.68 + 108.79 = 117.47 GHe.
To arrive: Substitute X into the equation derived in (a).
Useful for planning, e.g., in GCB Bank’s training budgets.
d) No, I would not use the line for a 2-month (approximately 60 days) training, as it involves extrapolation beyond the data range (maximum X=21 days). The relationship may not hold linearly for longer durations due to potential non-linear factors like capped allowances or different cost structures, leading to inaccurate predictions. In banking, extrapolating could misalign with actual costs, risking non-compliance with financial reporting standards.
- Uploader: Samuel Duah