1. Consider the following (familiar) equation which estimates the number of hours of sleep per year that someone gets as a function of hours worked per year (totwork), education (in years) and age. Suppose this equation is estimated using a new data set of 64 people and the results are
Sleep = 3434.8 - .118 totwork - 12.05 education +2.35 age
(115.71) (.025) (3.25) (1.01)
n = 64 R2 = 0.185
a. Test the null hypothesis that the coefficient on education is equal to 6 at the 596 level.
b. Dropping age and education from the equation yields the following estimate:
Sleep = 3288.0 - .127 totwork
(47.21) (.028)
n = 64 R2 = 0.141
Are education and age jointly significant at the 5% level? Justify your answer.
2. Consider the following relationship between number of pieces of candy eaten per day and pounds gained per month:
|
Person
|
Candy
|
Pounds
|
|
1
|
3
|
6
|
|
2
|
5
|
7
|
|
3
|
1
|
2
|
|
4
|
8
|
10
|
|
5
|
3
|
5
|
a. Estimate the relationship between candy and pounds using OLS. That is obtain the intercept and slope intercepts in the equation:
Pounds = β0 +β1Candy
b. What is the predicted number of pounds gained per month if someone eats 2 pieces of candy per day?
c. How much of the variation in pounds gained is explained by pieces of candy eaten? In other words: What is R2 for this regression?