Midterm: Please show your detailed clear and step by step -skipping steps are not Consider a fictitious dataset of n = 100 observations with s, = 80. We run a regression with three explanatory variables to get s = 50. a. Calculate the adjusted coefficient of determination, Ry b. Complete the ANOVA table. ANOVA Table Source Sum of Squares f Mean Square Repression Error Total C. Calculate the (unadjusted) coefficient of determination, R. 0.2 Consider a fictitious dataset of a = 100 observations with s, = 80. We run a regression with three explanatory variables to get s = 50. We also get 100 20 20 20 (XX)= 20 90 30 40 20 30 80 50 20 40 50 70 a. Determine the standard error of by. se(b, ). b. Determine the estimated covariance between by and by. c, Determine the estimated correlation between by and by. d. Determine the estimated variance of 4by + 3by.1.3 Consider the following small fictitious dataset. You will be fitting a regres- sion model to y using two explanatory variables, * and 42. From the fitted regression model. we have s = 1.373 and 0.15 0.53846 -0.07692 -0.15385 b = 0.692 and (X'X) = -0.07692 0.15385 -0.69231 2.88 -0.15385 -0.69231 4.11538 a. Write down the vector of dependent variables. y. and the matrix of explanatory variables, X. b. Determine the numerical value for 73, the fitted value for the third observation. c. Determine the numerical value for se(by). d. Determine the numerical value for rib, )