A car dealer is investigating how the value of a car depreciates over time. A random sample of eight

Question

A car dealer is investigating how the value of a car depreciates over time. A random sample of eight cars of the same model is selected and the current resale value, $y$ thousand dollars of each car is recorded along with its age in $x$ years. The results are shown in the table.

Age of car ($x$ years)	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Resale Value ($y$ thousand dollars)	$30.0$	$25.8$	$22.3$	$19.2$	$16.5$	$14.4$	$12.5$	$10.9$

Draw the scatter diagram for these values, labelling the axes clearly.[1]

It is thought that the resale value of a car, $y$, can be modelled by one of the formulae \[y = a + bx \quad \text{or} \quad \ln y = c + dx\]where $a$, $b$, $c$ and $d$ are real constants.

Find, correct to $5$ decimal places, the value of the product moment correlation coefficient between[2]
1. $y$ and $x$,
2. $\ln y$ and $x$.
Use your answers to parts (a) and (b) to explain which of $y = a + bx$ and $\ln y = c + dx$ is the better model.[2]

It is required to estimate the age of a car with a resale value of $\$18000$.

Find the equation of a suitable regression line and use it to find the required estimate.[2]
Without the use of a graphing calculator, re-write your equation from part (d) so that it can be used to estimate the resale value when the age is given in months.[2]

Accepted Answer

(b)(i) $r=-0.98751$ (ii) $r=-0.99984$ (c) $\ln y=c+dx$ (d) $x=3.48$ years (e) $\ln y=3.39-0.0121m$

2025 TMJC P2 Q9

2025 TMJC P2 Q9

Video Solution:

Solution:

Solution locked