The age, $t$ years, and weight, $w$ grams, of each of 10 coins were recorded - Edexcel - A-Level Maths Statistics - Question 5 - 2012 - Paper 1

The product moment correlation coefficient, $r$, is calculated using the formula:

$r = \frac{n \sum tw - \sum t \sum w}{\sqrt{\left(n \sum t^2 - (\sum t)^2 \right) \left(n \sum w^2 - (\sum w)^2 \right)}}$

Substituting the values:

After computation, we find: $r = -0.908469$ This rounds to $-0.908$.

To find the regression line, we first calculate the slope $b$:

$b = \frac{\sum(w - \bar{w})(t - \bar{t})}{\sum(t - \bar{t})^2}$

Using previously calculated values:

• ar{w} = 11.75, ar{t} = 268.8

Then, the equation format can be framed as:

$w = a + bt$

where $a = \bar{w} - b\bar{t}$.

The explanatory variable is the age of each coin, $t$. This is because the age is set and the weight varies.

To estimate the weight of a coin that is 5 years old, substitute $t = 5$ into the regression line equation:

$w = a + b(5)$

Using values obtained earlier, you can calculate the expected weight.

For an increase of 4 years in age, substitute $t$ value increase:

If the original age is $5$, then after 4 years, $t = 9$:

$w(9) - w(5) = b(9 - 5) = 4b$

Thus, the total effect is dependent on the value of $b$ computed previously.

Removing the fake coin, which has anomalously low weight for its age, will likely increase the product moment correlation coefficient. This is because it would reduce the overall variability in the sample, allowing for a more linear relationship between age and weight.