A psychology instructor wants to find out a suitable predictorof the Final examination marks of his students. He thinks that theAssignment marks or the Mid-term test marks can be used for thispurpose. However he is not sure which of those is more suitable.The following table shows the Assignment marks (out of 20),Mid-term test marks (out of 20) and the Final examination marks(out of 40) of 5 randomly selected students of his psychology classlast year. The data in a given row are related to the samestudent.
| student number | marks | mid term test marks | final exam marks |
| 1 | 14 | 11 | 23 |
| 2 | 17 | 15 | 40 |
| 3 | 20 | 20 | 40 |
| 4 | 10 | 11 | 29 |
| 5 | 16 | 13 | 35 |
Assuming that there is a linear relationship between theAssignment marks and the Final examination marks, calculate thePearson’s correlation coefficient. Round your answer to 3 decimalplaces
Assuming that there is a linear relationship between theMid-term test marks and the Final examination marks,
i. Derive the least squares prediction line to predict the Finalexamination marks based on the Mid-term test marks. (9 points)
ii. Calculate the coefficient of determination for the leastsquares prediction line. (3 points)
iii. Interpret the value of the coefficient of determination inrelation to this situation. (2 points)
Out of the two variables ‘Assignment marks’ and ‘Mid-term testmarks’, which variable is more suitable to use as the independentvariable in a least squares prediction line to predict the Finalexamination marks? Explain the reason for your answer. (
