11.1 Quick revision

We strongly 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:
  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.

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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.