- For the following questions, refer to the following equation and its respective graph
- What’s the value of $\hat\alpha_0 \ and\ \hat\alpha_1$?
- What’s the value of $\hat\alpha_0 \ and\ \hat\alpha_1$?

- $Y=\alpha_0+\alpha_1Treatment+\epsilon$

The following are questions that can help you hone in your understanding of a regression or your understanding of how to interpret regression.

When do countries tax wealth? Taxes are a big deal. they affect how people allocate their time, how much money government has, etc. Inheritance taxes are a particularly interesting tax policy because of the clear potential for conflict between rich and poor. Scheve and Stasavage (2012) investigated the sources of inheritance taxes by looking at tax policy and other characteristics of 19 countries for which data is available from 1816 to 2000. The data is measured every five years. Specifically the researchers looked at the relationship between inheritance taxes and who was allowed to vote. To assess if expanded suffrage led to increases or decreases in inheritance taxes, we can begin with the following model:

$Inheritance\ tax_{it}=\beta_0+\beta_1Expanded\ Suffrage_{i,t-1}+\epsilon_{it}$The dependent variable is the top inheritance tax rate, which is measure as a percent, and the independent variable is a dummy variable for whether all men were eligible to cote in at least half of the previous years.

- What does $\beta_0$ represents?
- What does $\beta_1$ represent?
- What’s the average difference in inheritance tax between expanded and not expanded suffrage?
- Let’s say you get:
- What’s the average inheritance tax for countries without expanded suffrage? Recall that units of inheritance tax are on percent from 0-100%
- What’s the average inheritance tax for countries with expanded suffrage?
- What’s the average difference in inheritance tax between expanded and not expanded suffrage?
- For the following questions refer to the following table. The outcome is inheritance tax rate.

- $Inheritance\ tax_{it}=4.75+19.33Expanded\ Suffrage_{i,t-1}$

- What’s the marginal effect of having universal suffrage on inheritance tax rate in column (d)?
- Write column (d) as an equation with numbers.

- In an effort to better understand the effects of “Get-out-the-vote” messages on voter turnout, Gerber and Green (2005) conducted an RCT involving approximately 30,000 individuals in New Haven, CT, in 1998. One of the treatments was randomly assigned in person visits in which a volunteer visited the person's home and encouraged him or her to vote. Table 3 reflects the findings from the RCT.

- What’s the marginal effect of being assign to in person contact on voting?
- Fill in the values of the following tables using the values from the table above $\begin{array}{c:c:c} \colorbox{yellow}{Regressions} & \text{Actually Contacted} & \text{Voted in 1998} \\ \hline \\ \text{Assigned to in-person contact} & \beta_1 & \alpha_1 \\ & \\ Constant & \beta_0 & \alpha_0 \end {array}$

8. Use the figure below to answer: What’s the sign of $\beta_2$ in the following equation? $Y=\beta_0+\beta_1X+\beta_2X^2$

9. Use the following figure to answer the following question. The main dependent variable on all the models is wages measured in hourly dollars, while height is measured in inches. The first column’s dependent variable is wages, second is wages, third is log(wages) and fourth is log (wages).

- Using column (1) What’s the relationship between adolescent height and wages?
- Using column (3) What’s the relationship between adolescent height and wages?
- Using column (1): Patricia grew about 5 inches between birthdays, how much is Patricia expected to earn now relative to her last birthday?
- What’s the interpretation of the coefficient 29.316 in column (2)
- What’s the interpretation of the coefficient 2.362 in column (4)
- I want to know how much wages increase in percent, when height increases by 15%, Which of these models would give me the quickest way to figure this out? and what’s the answer?
- I want to know how much wage increase in dollars when height increases by 20%, which of these models would give me the quickest way to figure this out? and what’s the answer?

- Energy Efficiency promises a double whammy of benefits: if we reduce the amount of energy we can both save the world and save money. What’s not to love? In this exercise we’ll dig into how to explore this relationship. The technology innovation is a programmable thermostat, which is a device that allows the user to preset temperatures at energy-efficient levels. Another important variable is HDD “heating degree-days”, which is a measure of how cold it was in the month (it is the number of degrees that a day’s average temperature is below 65 degree Fahrenheit). Usually the relationship between HDD and temperature (measure as Therms) is positive (the colder it gets, the higher the temperature people set their thermostat). We have data of houses that use thermostat and houses that don’t. The results from an OLS analysis are below, the main outcome variable for all of these regressions is “Therms”. The cost of a therm is $1.59 per therm. The cost of the thermostat is $60
- Using Model (a), What’s the main conclusion?
- Does you main conclusion change when accounting for HDD?
- Using results from model (b), how much money are houses who use thermostat saving? According to this model is the thermostat worth it?
- Does it make sense that the programmable thermostat should save $30 in the middle of the summer? This indicates that the cost-savings depend on the weather outside. It makes more sense to think about the effects of the thermostat with respect to temperature outside. Therefore we focus on model (c). What’s the interpretation of the number -0.48?
- Using Model (c), what is the effect of the thermostat when HDD is 500?
- Using Model (c) What’s the average therm use for houses that don’t have a thermostat is particular hot months?