A scientist investigated the link between the number of cancer cells killed by a certain drug and the strength of the drug used. The results were recorded and the coefficient of determination, r^{2}, was found to be 0.92.
Describe the relationship between the strength of drug used and the cancer cells killed.
Can we say that there is a causal relationship between the strength of drug used and the cancer cells killed.
Dave sells bicycles. He thinks that he sells more bicycles when there is a full moon. He recorded his number of sales during the different moon phases, and the resultant coefficient of determination r^{2} was found to be 0.19.
Describe the relationship between the phase of the moon and number of bicycles sold.
Can we say that there is a causal relationship between the phase of the moon and number of bicycles sold?
Mae has a small herb garden with a thyme plant. She suspects that the growth of the thyme plant is exponentially dependent on the amount of tea she drinks.
For a month she keeps a daily log of the amount of tea she drinks and the millimetres that the thyme plant has grown. The resultant coefficient of determination r^{2} was found to be 0.13.
Is there an exponential relationship between the growth of the thyme plant and the amount of tea that Mae drinks?
Can we say that there is a causal relationship between the growth of the thyme plant and the amount of tea that Mae drinks.
Shannon is convinced that the number of watch factories in a town is directly related to the number of department stores in that town. Shannon collects data on the number of watch factories and department stores in different towns across the country. The resultant coefficient of determination, r^{2}, was found to be 0.44.
Is the relationship between the number of department stores and the number of watch factories exponential or linear?
Does the number of department stores determine the number of watch factories?
Calculate the value of r^{2} for the following data sets whose correlation coefficient is given. Round your answer to two decimal places.
Correlation coefficient is - 0.61
Correlation coefficient is - 0.44
A linear association between two data sets is such that the correlation coefficient is - 0.72.
What proportion of the variation can be explained by the linear relationship? Round your answer to the nearest percent.
A linear association between two data sets is such that the coefficient of determination, r^{2} is 0.66.
Calculate the correlation coefficient if the relationship is positive. Round your answer to four decimal places.
Describe the strength of the linear relationship between the data sets.
A linear association between two data sets is such that the coefficient of determination, r^{2} is 0.80.
Calculate the correlation coefficient if the relationship is negative. Round your answer to four decimal places.
Describe the strength of the linear relationship between the data sets.
The following table shows the years of teaching experience for various teachers across Australia and their current salary:
Calculate the value of the correlation coefficient. Round your answer to two decimal places.
Hence, calculate the value of the coefficient of determination. Round your answer to four decimal places.
What percentage of the variation in teacher salaries can be explained by their years of teaching experience? Round your answer to two decimal places.
Comment on whether it is reasonable to suggest that teaching experience is the sole influence on teacher salaries.
| \text{Years of experience} | \text{Salary (\$)} |
|---|---|
| 5 | 72\,400 |
| 6 | 67\,200 |
| 6 | 65\,700 |
| 6 | 67\,400 |
| 5 | 73\,600 |
| 3 | 64\,500 |
| 10 | 87\,400 |
| 11 | 82\,000 |
| 1 | 57\,300 |
| 11 | 86\,900 |
| 11 | 84\,700 |
| 6 | 68\,800 |
During an alcohol education programme, 10 young adults were offered up to 12 drinks and were then given a simulated driving test where they scored a result out of a possible 100.
The results are displayed in the following table:
| Number of drinks | 2 | 3 | 5 | 3 | 4 | 2 | 7 | 6 | 9 | 2 |
|---|---|---|---|---|---|---|---|---|---|---|
| Driving Score | 61 | 65 | 44 | 62 | 36 | 73 | 32 | 41 | 18 | 54 |
Calculate the following. Round your answers to two decimal places.
The coefficient of determination
The correlation coefficient
What percentage of the variation in the driving score is accounted for by the number of drinks consumed? Round your answer to the nearest percent.
Comment on the claim “Clearly, the more you drink, the worse you drive.”
The heights (in \text{cm}) and the weights (in \text{kg}) of 8 primary school children are shown on the scattergraph:
Calculate the following. Round your answers to two decimal places.
What percentage of the variation in weight is accounted for by the height of the child? Round your answer to the nearest percent.
Comment on the claim “The weight of a child is primarily caused by their height.”
WhichBank is researching the number of applications they receive for home loans per day based on their advertised interest rate. The results are displayed in the following table:
Calculate the following. Round your answers to two decimal places.
The coefficient of determination
The correlation coefficient
What percentage of the variation in the number of applicants is accounted for by the interest rate? Round your answer to the nearest whole number.
Comment on the claim “If you want people to take out a home loan, then you need the interest rates to be low”.
| Interest rate | Number of applicants |
|---|---|
| 3.2 | 170 |
| 4.2 | 158 |
| 4.4 | 155 |
| 0.3 | 196 |
| 6.5 | 134 |
| 7.3 | 125 |
| 4.8 | 154 |
| 0.7 | 191 |
| 10.3 | 95 |
| 2.4 | 176 |
| 8.9 | 110 |
| 10.7 | 95 |
Advertisers are researching the optimal length of a UTube advertisement so that viewers don’t click 'Skip'.
The results in the table alongside show the length of the advertisement in minutes, and the number of proportion of viewers who clicked 'Skip':
Calculate the following. Round your answers to two decimal places.
Explain the meaning of the value of r^2 in context.
Comment on the claim “If a UTube ad is over 2 minutes in length it means everyone presses 'Skip' ”.
| Minutes | Proportion |
|---|---|
| 5.1 | 1 |
| 5.9 | 1 |
| 0.4 | 0.6 |
| 1.4 | 0.4 |
| 0.8 | 0.7 |
| 4 | 0.8 |
| 4.1 | 0.8 |
| 0.6 | 0.3 |
| 2.7 | 0.9 |
| 5.8 | 0.8 |
| 1.4 | 0.7 |
| 0.7 | 0 |
| 1.1 | 0.4 |
| 0.8 | 0.8 |
| 4.8 | 0.8 |