QCAA General Mathematics Bivariate data analysis 2
5 sample questions with marking guides and sample answers
A confounding variable is a variable that
can only take on a certain number of values.
remains constant throughout a statistical investigation.
is used to predict a difference in the response variable.
other than the explanatory variable, influences the response variable.
It is observed that as the number of ice blocks sold each month increases, the number of fans sold also increases. Which of these statements is therefore true?
There is a negative causation between the number of ice blocks sold and the number of fans sold each month.
There is a positive causation between the number of ice blocks sold and the number of fans sold each month.
There is a negative association between the number of ice blocks sold and the number of fans sold each month.
There is a positive association between the number of ice blocks sold and the number of fans sold each month.
Data was collected relating the number of hours spent fishing and the total number of fish caught.
The linear model for this data was found to be , where is the number of hours spent fishing, and is the total number of fish caught.
Use the model to predict the number of fish caught if 12 hours were spent fishing.
The correlation coefficient for this data is 0.688 and the coefficient of determination is 0.473. Use each of these to describe the strength of the linear association between the two variables and decide if your prediction is valid.
The table shows the profit made each year (in thousands of dollars) by a small business.
| Year | Profit ($'000s) |
|---|---|
| 2015 | 42.1 |
| 2016 | 36.9 |
| 2017 | 48.4 |
| 2018 | 52.3 |
| 2019 | 56.1 |
| 2020 | 59.8 |
Use a mathematical model to determine the equation of the least-squares line to fit this data.
Use the least-squares line to forecast the profit in 2021, to the nearest hundred dollars.
The table shows the number of sales for a small business in their first six months of trading.
| Time in months, | Number of sales, |
|---|---|
| 1 | 86 |
| 2 | 180 |
| 3 | 160 |
| 4 | 226 |
| 5 | 240 |
| 6 | 335 |
Use your calculator to determine the equation of the least-squares line.
Use the equation from Question 16a) to predict the number of sales in the 21st month.