## 11.1 Quick revision

We recommend trying these Quick revision questions before your tutorial.

A study of how weeds spread studied various factors about vehicles that might carry seeds. The researchers found a correlation between the number of grams of mud on a vehicle and the number of seeds carried by the vehicle.

In autumn, the correlation coefficient was given as $$r = 0.931$$

1. In this study, what variable would be the $$x$$ variable?
2. In this study, what variable would be the $$y$$ variable?
3. What is the value of $$R^2$$?
4. The regression equation is given as $$\hat{y} = 137.4 + 0.3459x$$. If 700 g of mud is found on the car, how many seeds are predicted to be carried by the vehicle?
5. In this regression equation, the slope means:
6. The $$P$$-value for the regression slope was $$0.002$$. What does this mean?
1. The $$x$$-variable (potentially) helps explains the values of the other variables... so the $$x$$-variable will be the number of grams of mud.
2. The $$y$$-variable is the number of seeds.
3. $$R^2 = (0.931^2) = 0.86676$$, or about 86.7%.
4. Using $$x = 700$$, we would have: $$\hat{y} = 137.4 + (0.3459\times 700) = 380$$ seeds.
5. The slope (which is $$0.3459$$) is how much the average value of $$y$$ changes (the number of seeds) when the value of $$x$$ (the amount of mud) increases by one.
6. The $$P$$-value is very small, which means that the slope in the sample is very unlikely to be non-zero simply by chance alone (remembering we initially assume that the population slope is zero).

### References

Khan I, Navie S, George D, O’Donnell C, Adkins SW. Alien and native plant seed dispersal by vehicles. Austral Ecology. Wiley Online Library; 2018;43(1):76–88.