5. A researcher is interested to see if there is a correlation in between the plot size (measured by the land area in m ) and plant dispersal rate (measured by number of plants) of ferns in a particular area. The results of the experiment are shown below: Area, x 5 8 13 19 25 27 34 40 46 Number of 20 15 37 51 42 59 67 73 64 ferns, y (a) Calculate the value of a and b for the least-square regression line and write the equation. (8 marks) (b) Calculate the value of the sample correlation coefficient, r. (2 marks) (c) Find the value of the coefficient of determination, r2. (1 mark) (d) Suppose that the researcher used a plot size of 31 m?: i. What would be the predicted value for the number of ferns. (2 marks) ii. Calculate its 95% confidence interval. (4 marks) (e) Test if there is any significant correlation between the plot size (measured by the land area in m") and plant dispersal rate (measured by number of plants) of ferns at a = 0.05. (8 marks)