A quant is instructed to investigate the relationship between the size of a bond issue y and its trading volumes (value traded) x. Consider the data for 7 bonds:

x 20 30 40 50 60 70 80

y 10 12 30 40 48 60 75

(b) A linear model of the form y = + x + is fitted to the data, where the error terms () independently follow a N(0, 2 ) distribution with the variance 2 being an unknown parameter.

(i) Determine the fitted line of the regression model.

(ii) Predict y when x = 250. (1)

(c) A partially completed ANOVA table for this regression analysis is given below.

Source of Sums of Degrees of Mean F-value

variation squares freedom squares

Regression 3,410 A D E

Error 59 B C

Total 3,469 6

(i) Determine the missing values A, B, C, D and E in the table.

(ii) Determine an estimate of the variance 2 based on the above table.

(iii) Perform an F-test to test the null hypothesis that there is no linear relationship between x and y, based on the above table.

(d) (i) Determine the percentage of variation in y explained by x.

(ii) Calculate the coefficient of correlation and give an interpretation.