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 corresponding E-statistic. Find the critical value from the F-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

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

x= 3^y

step-by-step explanation: