Question

Fixed effects can be estimated in three different ways. a- Use the lm command, include the time and country dummies. Hint: the easiest way to do this is to do lm(Y~X + year-1 + country-1) Remember to cluster you standard errors at the year and country. b- Demeaned the data manually and use the lm command to run an ols and your demeaned variables. Hint: Create a dataframe of demeaned variables. Remember the means are computed within country, not over the full set of observations. WB_demeaned <- with(WB_tidy, data.frame(lGDP = lGDP - ave(lGDP, country), edu = edu - ave(edu, country), year = year, country=country)) c- Use lpm to run a fixed effect model. Hint: You will need to specify the index, model and effect options. d- Produce a table of results for your ols, first difference and fixed effect models. What do you conclude?

Answer 1

In this scenario, the independent variable is the year the state entered the Union, and the dependent variable is the number of letters in a state name. A scatter plot can help visualize the relationship between the variables. The least-squares line equation can be calculated to determine the relationship's equation.

Step-by-step explanation:

a. Decide which variable should be the independent variable and which should be the dependent variable.

For the given scenario, the year the state entered the Union should be the independent variable, and the number of letters in a state name should be the dependent variable.

b. Draw a scatter plot of the data.

A scatter plot can be created with the year as the x-axis and the number of letters as the y-axis.

c. Does it appear from inspection that there is a relationship between the variables? Why or why not?

From the scatter plot, if there is a clear pattern or trend between the year and the number of letters, it suggests a relationship. If the points appear to form a linear or nonlinear pattern, it indicates a relationship. If the points are scattered randomly, it suggests no relationship.

d. Calculate the least-squares line. Put the equation in the form ý = a + bx.

The least-squares line equation can be determined using linear regression analysis, which minimizes the sum of the squared differences between the observed and predicted values. The equation will be in the form ŷ = a + bx, where ŷ is the predicted number of letters, a is the y-intercept, b is the slope, x is the year.

e. Find the correlation coefficient. What does it imply about the significance of the relationship?

The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1. A positive value indicates a positive relationship, while a negative value indicates a negative relationship. The closer the correlation coefficient is to -1 or 1, the stronger the relationship.

f. Find the estimated number of letters a state name would have if it entered the Union in 1900. Find the estimated number of letters a state name would have if it entered the Union in 1940.

Using the least-squares line equation, substitute the corresponding years to estimate the number of letters.

g. Does it appear that a line is the best way to fit the data? Why or why not?

From the scatter plot and analysis, if the relationship between the variables appears linear and the correlation coefficient indicates a significant linear relationship, a line may be a reasonable fit for the data. However, further analysis and consideration of other factors may be necessary to determine the best way to fit the data.