5. A researcher is interested to see if there is a correlation in between the plot size (measured by the land area in m2) 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 ferns, y 20 15 37 51 42 59 67 73 64 (a) Calculate the value of a and b for the least-square regression line and write the equation. (b) Calculate the value of the sample correlation coefficient, r. (c) Find the value of the coefficient of determination, r2. (d) Suppose that the researcher used a plot size of 31 m2: i. What would be the predicted value for the number of ferns. ii. Calculate its 95% confidence interval. (e) Test if there is any significant correlation between the plot size (measured by the land area in m2) and plant dispersal rate (measured by number of plants) of ferns at = 0.05