f. What fraction of the total variation in Y is explained by the regression? 7. A simple linear regression equation, Y = a + bX, is estimated by a computer prog which produces the following output: CHAPTER 4 Basic Estimation Techniques 151 DEPENDENT VARIABLE : Y R - SQUARE F - RATIO P - VALUE ON F OBSERVATIONS : 25 0. 7482 68. 351 0 . 00001 PARAMETER VARIABLE STANDARD ESTIMATE ERROR T - RATIO P - VALUE INTERCEPT 325 . 24 125 . 09 2. 60 0 . 0160 X 0. 8057 0. 2898 2. 78 0. 0106 a. How many degrees of freedom does this regression analysis have? b. What is the critical value of t at the 5 percent level of significance? c. Test to see if the estimates of a and b are statistically significant. d. Discuss the p-values for the estimates of a and b. e. How much of the total variation in Y is explained by this regression equation? How much of the total variation in Y is unexplained by this regression equation? f. What is the critical value of the F-statistic at a 5 percent level of significance? Is the overall regression equation statistically significant? g. If X equals 100, what value do you expect Y will take? If X equals 0? 8. Evaluate each of the following statements