11.1 Quick revision

We recommend trying these Quick revision questions before your tutorial.

A study of how weeds spread (Khan et al. 2018) 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.