Q1. The lung capacities (in milliliters) of 50 men randomly sampled from a large population of workers were measured in order to learn about the effects of smoking (measured in packs per day), age (in years), and height (in inches). The regression of lung capacity on age, height and smoking was conducted and produced the following results:
|
Variable
|
Coefficient
|
Std. Error
|
95% CI
|
|
(Intercept)
|
345.4
|
38.1
|
[268.7, 422.1]
|
|
Age
|
-39.0
|
9.1
|
[-57.3, -20.7]
|
|
Height
|
98.4
|
32.0
|
[34.0, 162.8]
|
|
Smoking
|
-180.0
|
206.4
|
[-595.5, 235.5]
|
(a) Other things being equal, what would you estimate is the effect on lung capacity of:
i. Smoking 1 pack per day?
ii. Being 5 years older?
iii. Smoking 2 packs per day and being 10 years older?
(b) Graph predicted relationship between age and lung capacity for a five foot tall nonsmoker (recall that height is measured in inches for the regression).
(c) On the same plot from (c), draw a dashed line plotting the predicted relationship between age and lung capacity for a six foot tall non-smoker.
(d) As far as lung capacity is concerned, the effect of smoking 1 pack of cigarettes per day is the same as aging how many years?
(e) Fill in the last column of this table by constructing a 95% confidence interval for each estimated parameter (the intercept and the three coefficients).
Q2. The table below contains estimates from a linear regression predicting respondents' opinions on an abortion views scale going from 0 to 10 where higher values indicate more pro-choice views and lower values indicate more pro-life views with the independent variables "female" and "HS grad", which are dummy variables for whether the respondent is female and whether they graduate high school. The data have 1,716 observations in total.
|
Variable
|
Coefficient
|
Std. Error
|
|
(Intercept)
|
4.04
|
.31
|
|
Female
|
.28
|
.13
|
|
HS Grad
|
1.21
|
.24
|
(a) What does the estimated intercept represent in this regression?
(b) What does the estimated coefficient on Female represent here?
(c) What does the estimated coefficient on HS Grad represent here?
(d) Test the hypothesis that the coefficient on Female is zero at the .05 significance level.
(e) Test the hypothesis that the coefficient on HS Grad is zero at the .05 significance level.
Q3. The table below contains estimates from a linear regression predicting respondents' views on an abortion views scale going from 0 to 10 where higher values indicate more pro-choice views and lower values indicate more pro-life views with the independent variables "female", "HS grad" and an interaction between the two. The data have 1,716 observations in total. (This is the same data as in question 2 above, but with a different regression model estimated).
|
Variable
|
Coefficient
|
Std. Error
|
|
(Intercept)
|
4.04
|
.31
|
|
Female
|
-.55
|
.28
|
|
HS Grad
|
1.09
|
.36
|
|
Female x HS Grad
|
1.16
|
.48
|
(a) What does the estimated intercept represent in this regression?
(b) What does the estimated coefficient on Female represent here?
(c) What does the estimated coefficient on HS Grad represent here?
(d) What does the estimated coefficient on Female x HS Grad represents here?
(e) What is the predicted abortion scale value for a male without a HS degree?
(f) What is the predicted abortion scale value for a female without a HS degree?
(g) What is the predicted abortion scale value for a male with a HS degree?
(h) What is the predicted abortion scale value for a female with a HS degree?
Q4. Imagine you have a model predicting ideology (where -1 is extremely liberal, 1 is extremely conservative and values can range anywhere between these two extremes) with income (in thousands of dollars per year) and a dummy variable for White that equals 1 for White respondents and 0 for respondents of any other race.
Assume that the following are the estimated coefficients for each variable:
|
|
Estimate
|
|
Intercept
|
-.3
|
|
Income (in thousands of $)
|
0
|
|
White
|
.1
|
|
Income x White
|
.01
|
[Note: These estimates are made up for teaching purposes, not based on any real data.]
(a) Draw a plot with x-axis labeled "Income (in thousands of $)", which goes from 0 to 100 and y-axis labeled "Ideology", which goes from -1 to 1. Graph the predicted relationship between income and ideology for non-Whites using a solid line.
(b) Add a dashed line to your plot above showing the predicted relationship between income and ideology for Whites.
(c) Briefly describe in words what the coefficient values tell you about the effects of income and how they vary by race. (Note: you can ignore statistical significance here and treat the estimates as if they were "correct" since the aim here is just to understand what the estimated values would imply.)