# PC Labs for SO5041: Week 11

## Table of Contents

## 1 Week 11 Lab: Correlation and 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
R^{2} 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 R^{2} is big, the independent variable "explains" the
dependent variable "a lot". However, it is possible for R^{2} 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.