IB Math EE Guidance

Content-specific conceptual understandings

Linear correlation of bivariate data.
Pearson’s product-moment correlation coefficient, r.

Technology should be used to calculate r. However, hand calculations of r may enhance understanding.
Critical values of r will be given where appropriate.
Students should be aware that Pearson’s product moment correlation coefficient (r) is only meaningful for linear relationships.

Scatter diagrams; lines of best fit, by eye, passing through the mean point.

Positive, zero, negative; strong, weak, no correlation.
Students should be able to make the distinction between correlation and causation and know that correlation does not imply causation.

Equation of the regression line of y on x.
Use of the equation of the regression line for prediction purposes.
Interpret the meaning of the parameters, a and b, in a linear regression y=ax+b.

Technology should be used to find the equation.
Students should be aware:
• of the dangers of extrapolation
• that they cannot always reliably make a prediction of x from a value of y, when using a yon x line.

Exercises

1. The maximum temperature  T , in degrees Celsius, in a park on six randomly selected days is shown in the following table. The table also shows the number of visitors,  N , to the park on
   each of those six days.The relationship between the variables can be modelled by the regression equation  N = aT + b .
   1. Find the value of  a  and of  b
   2. Write down the value of  r
   3. Use the regression equation to estimate the number of visitors on a day when the maximum temperature is 15ºC.
2. The following table shows values of ln x and ln y.The relationship between ln x and ln y can be modelled by the regression equation ln y = a ln x + b.
   1. Find the value of a and of b
   2. Use the regression equation to estimate the value of y when x = 57

   The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0, n ≠ 0, n ≠ 1.

   1. By expressing ln y in terms of ln x, find the value of n and of k.
3. The following table shows the hand lengths and the heights of five athletes on a sports team.The relationship between x and y can be modelled by the regression line with equation y = ax + b.
   1. Find the value of a and of
   2. Write down the correlation coefficient.
   3. Another athlete on this sports team has a hand length of 5cm. Use the regression equation to estimate the height of this athlete.
4. Adam is a beekeeper who collected data about monthly honey production in his bee hives.The relationship between the variables is modelled by the regression line with equation P = aN + b
   1. Write down the value of a and of b
   2. Use this regression line to estimate the monthly honey production from a hive that has 270 bees
5. The following table shows the mean weight, y kg, of children who are x years old.The relationship between the variables is modelled by the regression line with equation y = ax + b.
   1. Find the value of a and of b
   2. Write down the correlation coefficient.
   3. Use your equation to estimate the mean weight of a child that is 1.95 years old.