Consider a situation where economic theory suggests that you impose certain restrictions on your estimated multiple regression function. These may involve the equality of parameters, such as the returns to education and on the job training in earnings functions, or the sum of coefficients, such as constant returns to scale in a production function. To test the validity of your restrictions, you have your statistical package calculate the correspondingF-statistic. Find the critical value from theF-distribution at the 5% and 1% level, and comment whether or not you will reject the null hypothesis in each of the following cases. Make sure you illustrate graphically all your tests.

(a) number of observations: 152; number of restrictions: 3;F-statistic: 3.21

(b) number of observations: 1,732; number of restrictions:7;F-statistic: 4.92

(c) number of observations: 63; number of restrictions: 1;F-statistic: 2.47

(d) number of observations: 4,000; number of restrictions: 5;F-statistic: 1.82