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- The 95% confidence interval for the coefficient on income is B^1 – tc• SE (B^1) < B1 < B^1 + tc• SE (B^1),
- The 95% confidence interval is 0.0114 < B1 < 0.0340.
- There is 95% chance that the true value of B is in the above range.
2. #17, Page 63
- a. Adjusted R2 = 1 – (1 – 0.7) • (9/5) = 0.
- b. Adjusted R2 = 1 – (1 – 0.7) • (19/15) = 0.
- c. Adjusted R2 = 1 – (1 – 0.7) • (99/95) = 0.
- d. With the same R2, when the sample number goes up, adjusted R2 will increase. The implication here is that when you add more observations to your sample, the degrees of freedom goes up, and therefore the goodness of fit will increase.
- e. When the sample size is increased, R2 may increase, decrease or even stay the same. It depends on how well the new observations fit the regression line.
Percentage change
- Is equal to (new value- old value) divided
by the old value.
Year Real Tax Collection % Change in Nominal Tax Collections
% Percent in Real Tax Collections
1990 419,
1991 401,564 -0.25 -4.
1992 402,363 3.25 0.
1993 410,958 5.17 2.
1994 421,968 5.34 2.
1995 449,880 9.60 6.
1996 481,243 10.12 6.
1997 528,101 12.30 9.
1998 576,898 10.93 9.
1999 619,312 9.71 7.35 Docsity.com
4. #5, Page 82
- The model is a tautology, or it is very close to being a tautology. The right hand side simply adds up all the people who have left the nursing home for various reasons. The true value for each of the slope coefficients will always be 1. For example, if one more person leaves the nursing home to live with relatives, EXIT will always increase by 1, so the true value of B3 is
- This is true for all the slope coefficients.
5. #6, Page 83
- a. HOUSE_EXP = 7 + 0.00017 INCOME
- b. HOUSE_EXP = 7,000 + 170 INCOME
- c. HOUSE_EXP = 7 + 0.17 INCOME
- d. HOUSE_EXP = 0.7 + 0.17 INCOME
- e. “b” is the easiest to interpret. You can say that if someone has an additional 1,000 in income, on average, they will spend $170 more on housing that year.
- f. A measure of the price of housing, and the number of people in the household are two possible answers.
Some elementary rules of partial differentiation
- Y = 2X 1 + 3 X 1 X 2 + 5 X 33
- dY/dX 1 measures change in Y as a result
of one unit change in X1 assuming X2 and
X3 are constant
- dY/dX 1 = 2 +3X (^2)
- dY/dX 2 = 3X (^1)
- dY/dX 3 = 15X 32
Intercept Dummies
• Theory 1: Men’s earnings is ,in
general, higher than women’s
earnings
- How would a dummy variable capture
this?
- Intercept dummy
- Earnings = B 0 + B 1 (gender) + B 2 (years of work) + error - Where gender is dummy variable that takes a value of 1 if the observation is a male and 0 otherwise.
So you add one more variable to your data
set. Suppose you have 5 observations in
your data set, then it will look like this
Observation Earnings Years of work
Gender
- female 0
- male 1
- male 1
- female 0
- male 1
How much more?
- If your observation is a male
- Earnings^ = 1000+ 200 (1) + 500 (years of work)
- Earnings^ = 1200+ 500 (years of work)
- If your observation is female
- Earnings^ = 1000+ 200 (0) + 500 (years of work)
- Earnings^ = 1000+ 500 (years of work)
Graph of earnings versus experience
Years of work
Earnings
Female
Male
1000
1200
Graph of earnings versus experience
Years of work
Earnings
Female
Male
How would a dummy variable capture this?
- Slope dummy
- Earnings = B 0 + B 1 (years of work) + B 2 (years of work) *( gender) + error - Where gender is dummy variable that takes a value of 1 if the observation is a male and 0 otherwise.
