Objective

Today you will:

Develop a research question using real data
Estimate a simple linear regression in R
Create a graph illustrating the relationship
Summarize your findings in a clean results table
Reflect on important econometric issues
Share your findings with your classmate(s)

You may only estimate: \[Y_i = \beta_0 + \beta_1 X_i + u_i\]

No multiple regression (yet!). Please also avoid using variables listed as factors or categorical variables in your regressions; we have only covered continuous variables in class so far.

Step 1: Dataset Selection

Please select one of the following datasets. The R code to load the data into R, and a brief description of the variables is provided below for each dataset:

Australian Health Service Utilization Data

Cross-section data originating from the 1977–1978 Australian Health Survey.

Variables:

visits Number of doctor visits in past 2 weeks.
gender Factor indicating gender.
age Age in years divided by 100.
income Annual income in tens of thousands of dollars.
illness Number of illnesses in past 2 weeks.
reduced Number of days of reduced activity in past 2 weeks due to illness or injury.
health General health questionnaire score using Goldberg’s method.
private Factor. Does the individual have private health insurance?
freepoor Factor. Does the individual have free government health insurance due to low income?
freerepat Factor. Does the individual have free government health insurance due to old age, disability or veteran status?
nchronic Factor. Is there a chronic condition not limiting activity?
lchronic Factor. Is there a chronic condition limiting activity?

library(pacman)
p_load(AER)
data("DoctorVisits")
head(DoctorVisits)

##   visits gender  age income illness reduced health private freepoor freerepat
## 1      1 female 0.19   0.55       1       4      1     yes       no        no
## 2      1 female 0.19   0.45       1       2      1     yes       no        no
## 3      1   male 0.19   0.90       3       0      0      no       no        no
## 4      1   male 0.19   0.15       1       0      0      no       no        no
## 5      1   male 0.19   0.45       2       5      1      no       no        no
## 6      1 female 0.19   0.35       5       1      9      no       no        no
##   nchronic lchronic
## 1       no       no
## 2       no       no
## 3       no       no
## 4       no       no
## 5      yes       no
## 6      yes       no

Cost Function of Electricity Producers 1970

Cross-section data, at the firm level, on electric power generation.

Variables:

cost total cost.
output total output.
labor wage rate.
laborshare cost share for labor.
capital capital price index.
capitalshare cost share for capital.
fuel fuel price.
fuelshare cost share for fuel.

library(pacman)
p_load(AER)
data("Electricity1970")
head(Electricity1970)

##      cost output   labor laborshare capital capitalshare   fuel fuelshare
## 1  0.2130      8 6869.47     0.3291  64.945       0.4197 18.000    0.2512
## 4  3.0427    869 8372.96     0.1030  68.227       0.2913 21.067    0.6057
## 5  9.4059   1412 7960.90     0.0891  40.692       0.1567 41.530    0.7542
## 14 0.7606     65 8971.89     0.2802  41.243       0.1282 28.539    0.5916
## 15 2.2587    295 8218.40     0.1772  71.940       0.1623 39.200    0.6606
## 16 1.3422    183 5063.49     0.0960  74.430       0.2629 35.510    0.6411

US General Social Survey 1974–2002

Cross-section data for 9120 women taken from every fourth year of the US General Social Survey between 1974 and 2002 to investigate the determinants of fertility.

Variables:

kids Number of children. This is coded as a numerical variable but note that the value 8 actually encompasses 8 or more children.
age Age of respondent.
education Highest year of school completed.
year GSS year for respondent.
siblings Number of brothers and sisters.
agefirstbirth Woman’s age at birth of first child.
ethnicity Factor indicating ethnicity. Is the individual Caucasian (“cauc”) or not (“other”)?
city16 Factor. Did the respondent live in a city (with population \(>\) 50,000) at age 16?
lowincome16 Factor. Was the income below average at age 16?
immigrant Factor. Was the respondent (or both parents) born abroad?

library(pacman)
p_load(AER)
data("GSS7402")
head(GSS7402)

##   kids age education year siblings agefirstbirth ethnicity city16 lowincome16
## 1    0  25        14 2002        1            NA      cauc     no          no
## 2    1  30        13 2002        4            19      cauc    yes          no
## 3    1  55         2 2002        1            27      cauc     no          no
## 4    2  57        16 2002        1            22      cauc     no          no
## 5    2  71        12 2002        6            29      cauc    yes          no
## 6    0  19        13 2002        1            NA     other    yes          no
##   immigrant
## 1        no
## 2        no
## 3       yes
## 4        no
## 5        no
## 6        no

Medicaid Utilization Data

Cross-section data originating from the 1986 Medicaid Consumer Survey.

Variables:

visits Number of doctor visits.
exposure Length of observation period for ambulatory care (days).
children Total number of children in the household.
age Age of the respondent.
income Annual household income (average of income range in million USD).
health1 The first principal component (divided by 1000) of three health-status variables: functional limitations, acute conditions, and chronic conditions.
health2 The second principal component (divided by 1000) of three health-status variables: functional limitations, acute conditions, and chronic conditions.
access Availability of health services (0 = low access, 1 = high access).
married Factor. Is the individual married?
gender Factor indicating gender.
ethnicity Factor indicating ethnicity (“cauc” or “other”).
school Number of years completed in school.
enroll Factor. Is the individual enrolled in a demonstration program?
program Factor indicating the managed care demonstration program: Aid to Families with Dependent Children (“afdc”) or non-institutionalized Supplementary Security Income (“ssi”).

library(pacman)
p_load(AER)
data("Medicaid1986")
head(Medicaid1986)

##   visits exposure children age income health1 health2 access married gender
## 1      0      100        1  24 14.500   0.495  -0.854   0.50      no female
## 2      1       90        3  19  6.000   0.520  -0.969   0.17      no female
## 3      0      106        4  17  8.377  -1.227   0.317   0.42      no female
## 4      0      114        2  29  6.000  -1.524   0.457   0.33      no female
## 5     11      115        1  26  8.500   0.173  -0.599   0.67      no female
## 6      3      102        1  22  6.000  -0.905   0.062   0.25      no female
##   ethnicity school enroll program
## 1      cauc     13    yes    afdc
## 2      cauc     11    yes    afdc
## 3      cauc     12    yes    afdc
## 4      cauc     12    yes    afdc
## 5      cauc     16    yes    afdc
## 6     other     12    yes    afdc

Determinants of Murder Rates in the United States

Cross-section data on states in 1950.

Variables:

rate Murder rate per 100,000 (FBI estimate, 1950).
convictions Number of convictions divided by number of murders in 1950.
executions Average number of executions during 1946–1950 divided by convictions in 1950.
time Median time served (in months) of convicted murderers released in 1951.
income Median family income in 1949 (in 1,000 USD).
lfp Labor force participation rate in 1950 (in percent).
noncauc Proportion of population that is non-Caucasian in 1950.
southern Factor indicating region.

library(pacman)
p_load(AER)
data("MurderRates")
head(MurderRates)

##    rate convictions executions time income  lfp noncauc southern
## 1 19.25       0.204      0.035   47   1.10 51.2   0.321      yes
## 2  7.53       0.327      0.081   58   0.92 48.5   0.224      yes
## 3  5.66       0.401      0.012   82   1.72 50.8   0.127       no
## 4  3.21       0.318      0.070  100   2.18 54.4   0.063       no
## 5  2.80       0.350      0.062  222   1.75 52.4   0.021       no
## 6  1.41       0.283      0.100  164   2.26 56.7   0.027       no

Step 2: Formulate a Research Question

Write your research question clearly: “Is there a linear relationship between ______ and ______?”

Define:

Y (dependent variable):
X (independent variable):
Expected sign of \(\beta_1\) (positive or negative?)
Explain briefly why you expect this sign.

Step 3: Create a Scatterplot

Examine the scatterplot of your data. Does the relationship look linear? Are there outliers?

Step 4: Estimate the Model

Estimate your regression model. Present the results in a table that reports:

Estimated intercept
Estimated slope
Standard errors
\(R^2\)

Step 5: Interpret Your Results

In complete sentences:

Interpret the slope coefficient.
Is the coefficient statistically significant?
Is the magnitude economically meaningful?
What does \(R^2\) tell you here?

Step 6: Econometric Considerations

Even though we are using simple OLS, we must think carefully.

Consider the following:

What important variables might affect Y that are not in your model? Would those omitted factors likely be correlated with X? (Omitted Variable Bias)
Could Y cause X instead of X causing Y? (Reverse Causality)
Can you generalize your results? (External Validity)

Step 7: Share

Share your results with a classmate.

Step 8: Submit Work

Before you leave today, please submit your written worksheet to me and upload your R script to the in-class Canvas assignment for today.

Simple OLS R Activity

Jenni Putz

2026-02-17

Objective

Step 1: Dataset Selection

Australian Health Service Utilization Data

Cost Function of Electricity Producers 1970

Medicaid Utilization Data

Determinants of Murder Rates in the United States

Step 2: Formulate a Research Question

Step 3: Create a Scatterplot

Step 4: Estimate the Model

Step 5: Interpret Your Results

Step 6: Econometric Considerations

Step 8: Submit Work