| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2004 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Calculate regression line then predict |
| Difficulty | Moderate -0.8 This is a straightforward application of standard regression formulas with all summary statistics provided. Students simply substitute into b = S_xy/S_xx and a = ȳ - bx̄, then use the line for prediction. No conceptual difficulty or problem-solving required, just routine calculation—easier than average A-level questions. |
| Spec | 5.09a Dependent/independent variables5.09b Least squares regression: concepts5.09c Calculate regression line |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(b = \frac{S_{xy}}{S_{xx}} = \frac{3477.6}{4402} = 0.7900...\) | B1 | awrt 0.79 |
| \(a = \bar{y} - b\bar{x} = 28.6 - (0.7900...)\times 36 = 0.159836...\) | B1 | awrt 0.16 |
| \(y = 0.16 + 0.79x\) | B1\(\int\) | or equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| OR just answer B1 ONLY | ||
| \(y = 0.16 + 0.79 \times 45 = 35.71\) | B1 | awrt 35.7 |
## Question 2:
### Part (a):
| Working | Mark | Guidance |
|---------|------|----------|
| $b = \frac{S_{xy}}{S_{xx}} = \frac{3477.6}{4402} = 0.7900...$ | B1 | awrt 0.79 |
| $a = \bar{y} - b\bar{x} = 28.6 - (0.7900...)\times 36 = 0.159836...$ | B1 | awrt 0.16 |
| $y = 0.16 + 0.79x$ | B1$\int$ | or equivalent |
### Part (b):
| Working | Mark | Guidance |
|---------|------|----------|
| OR just answer B1 ONLY | | |
| $y = 0.16 + 0.79 \times 45 = 35.71$ | B1 | awrt 35.7 |
---2. An experiment carried out by a student yielded pairs of $( x , y )$ observations such that
$$\bar { x } = 36 , \quad \bar { y } = 28.6 , \quad S _ { x x } = 4402 , \quad S _ { x y } = 3477.6$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the equation of the regression line of $y$ on $x$ in the form $y = a + b x$. Give your values of $a$ and $b$ to 2 decimal places.
\item Find the value of $y$ when $x = 45$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2004 Q2 [4]}}