PC Labs for SO5041: Week 11

Table of Contents

1 Week 11 Lab: Regression

1.1 Correlation

The following data file contains six pairs of variables, X1 and Y1, X2 and Y2 etc. 

use http://teaching.sociology.ul.ie/so5041/labs/correl

First, graph all six pairs in scatterplots. Also graph X1 with Y2. What sort of association do you see in each case (positive, negative, none, strong, weak)? Make a guess what the value of the correlation coefficient might be (write it down).

For each graph, get the correlation coefficient: e.g., corr x1 y1. How do the reported correlation coefficients correspond with those you guessed?

1.2 Correlations with real data

With the following data file (use http://teaching.sociology.ul.ie/so5041/ocorr), explore the correlations between the variables it contains, graphically and with the correlation coefficient.

1.3 Linear Regression

Do sysuse nlsw88 to load the National Longitudinal Study of Women data set that comes with Stata. Look at wage, the hourly wage rate. Predict wage using grade:

reg wage grade

Write out the Y = a + bx equation. Calculate the predicted value for grade=0 and grade=20, and draw the line on a graph (on paper).

1.4 R-squared

Considering the following list of variables:

  • age
  • ttl_exp, total lifetime work experience
  • tenure, tenure in current job
  • grade, years of education
  • union, whether a member of a union

Let's consider wage as the "dependent variable", to be explained by the others (ignoring union for the moment as it only has two values). Create scatterplots for wage (on the Y-axis) compared with each of the other variables. Consider the correlations too (e.g., =corr age wage =Can you see much of a relationship?

Now do regression analyses: reg wage varname, with each of the other variables one at a time as the independent. There are two things to look at: the R2 figure and the parameter estimate (B for the independent variable, along with its significance). Which variables affect wage much? Do any not affect it at all?

Interpret the results: in each case ask the question, "what happens to the predicted value of income, if the value of X were to change by one unit?". For two different values of the independent variable (X) calculate the predicted value of income – see where these fall on the scatterplot, and see where the regression line would lie. Does it seem like a good summary of the relationship?

If R2 is big, the independent variable "explains" the dependent variable "a lot". However, it is possible for R2 to be small and yet for the independent variable to a systematic effect (i.e. very low p-value for significance): this independent variable may be only one thing among many that affect the dependent variable.

1.4.1 Union effects

Test the effect of union on wage. Use a t-test in the first instance, and then fit a regression. Compare the results.

Do the same relating grade to union. Note that unionised workers tend to earn more and be better educated. Could it be that the union effect is simply due to them being better educated? That is, for workers with similar education does union status matter?

Fit the wage/grade regression for unionised and non-unionised workers separately, and think about the results (make scatterplots too): do reg wage grade if union==0, reg wage grade if union==1.

1.4.2 Two explanatory variables

You can also fit a model with both union status and grage explaining wage. Fit a regression with both grade and union as explanatory variables. Interpret the parameter estimates.

Draw the regression lines for union members and non-union members.

Compare your results to the previous separate regressions, and the t-test.