5 Consider a regression model in which the response variable Y; is linked to the explanatory variable X, by the following equation: Y,= a + bX+e, i= 1, ..., n assuming that the error terms ei are independent and Normally distributed with expectation 0 and variance o. In a sample of size n= 10, the following statistics have been observed: x; = 141, Y; = 127, 1 i=1 n1 11 ? = 2,014, = 1,629, xiy = 1,810. i=1 =1 (i) Calculate values for Sxx, Syy, and Sxy [3] (ii) Write down, using your answers to part (i), the value of Pearson's correlation coefficient between the variables X and Y. [1] (iii) Calculate estimates of the parameters a and b in the regression model. [2] [Total 6] 5 Consider a regression model in which the response variable Y; is linked to the explanatory variable X, by the following equation: Y,= a + bX+e, i= 1, ..., n assuming that the error terms ei are independent and Normally distributed with expectation 0 and variance o. In a sample of size n= 10, the following statistics have been observed: x; = 141, Y; = 127, 1 i=1 n1 11 ? = 2,014, = 1,629, xiy = 1,810. i=1 =1 (i) Calculate values for Sxx, Syy, and Sxy [3] (ii) Write down, using your answers to part (i), the value of Pearson's correlation coefficient between the variables X and Y. [1] (iii) Calculate estimates of the parameters a and b in the regression model. [2] [Total 6]