A second hand car dealer has 10 cars for sale - Edexcel - A-Level Maths Statistics - Question 4 - 2008 - Paper 1

To find the least squares regression line:

1. Calculate the slope $b$ using the formula: $b = \frac{n \sum xy - \sum x \sum y}{n \sum x^2 - (\sum x)^2}$
   where $n = 10$, $\sum xy = 1818.5$, $\sum x = 41$, $\sum y = 406$, and $\sum x^2 = 188$. Substituting the values yields: $b = \frac{10(1818.5) - (41)(406)}{10(188) - (41)^2} = 7.73 (approximately)$

2. Calculate the intercept $a$ using: $a = \frac{\sum y - b \sum x}{n}$
   Substituting gives: $a = \frac{406 - 7.73(41)}{10} = 8.89 (approximately)$

Thus, the regression equation is: $y = 7.73x + 8.89$.

The slope $b = 7.73$ indicates that for each additional year in the age of the car, the mileage is expected to increase by approximately 7.73 thousand miles.

To find the predicted mileage for a 5 year old car, substitute $x = 5$ into the regression equation: $y = 7.73(5) + 8.89 = 48.00$
Thus, the predicted mileage is 48 thousand miles.