Use the answer to QUESTION 1.1 to write down the estimated average yearly decrease in the selling price of these 11 cars.
About this question
Question 1.4 of Mathematics Grade 12 Paper 2, NSC Examination (DBE, November 2025). It tests the Term 3 ATP topic Statistics (Regression and Correlation).
- TermTerm 3
- ATP topicStatistics (Regression and Correlation)
- PaperPaper 2
- Marks1 mark
There were 11 cars of the same model for sale at a car dealership. The age (in years) of each car and its selling price (in rands) are given below.
| Age of car (years) | 2 | 3 | 3 | 4 | 4 | 4 | 6 | 6 | 7 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Selling price (R) | 293 000 | 265 000 | 256 000 | 219 000 | 241 000 | 246 000 | 226 000 | 176 000 | 154 000 | 180 000 | 148 000 |
The gradient \(b = -22\,988{,}32\) gives the change in price per year.
R22 988,32 per year
More Questions On Statistics (Regression and Correlation)
This is a strong negative correlation, so the points lie close to the regression line.
The prediction is valid.
Enter the data in the calculator in statistics (linear regression) mode.
\[a = 39{,}456\ldots \approx 39{,}46\]\[b = -0{,}590\ldots \approx -0{,}59\]\(\hat{y} = 39{,}46 - 0{,}59x\)
About \(22{,}35\) push-ups (so about 22 push-ups)
Enter the data in the calculator in STAT mode (A + BX), with \(x\) = age and \(y\) = price.
\[a = 331\,397{,}20\]\[b = -22\,988{,}32\]\(\hat{y} = 331\,397{,}20 - 22\,988{,}32x\)
\(Q_1\) position:
\[\frac{1}{4} \times 60 = 15\text{th value}\]\(Q_1 \approx 44\) minutes
Plot two points from the equation, for example:
\(x = 90\):
\[\hat{y} = -43{,}72 + 2{,}36(90) = 168{,}68\]\(x = 150\):
\[\hat{y} = -43{,}72 + 2{,}36(150) = 310{,}28\]Join the points with a straight line that covers the data range, from about \(x = 85\) to \(x = 160\).