In SOC345/lehmansociology: Tools for Sociology Students Using R

# Load your libraries here

library('lehmansociology')
library('ggplot2')

In this lab we are going to use a famous data set to understand a bit more about regession analysis.
Some of the issues we want to think about are: What is regression? What assumptions does regression analysis have? How do we interpret the results of regression? What is the role of plots in doing regression

For this project we will be using the data set called anscombe. You can see the data set in RStudio by typing View(anscombe) in your console. Remember that you can't knit View() so don't put that in your code chunk.

The anscombe data set has 4 x variables, x1, x2, x3, x4 and 4 y variables, y1, y2, y3 and y4.

Lets start by looking more closely at them.

# Print the whole data set by just typing the name.


# Get a summary of all of the variables in the data set.

Working with one or two partners, list at least 5 interesting facts about the

data.

These don't have to be big things, just show you have looked closely.

Now let's run a ordinary least squares (OLS) regression analyses with each of the pairs (x1 with y1 etc). We will use the lm() function which is lm(dependent_variable ~ independent_variable, data=datasetname) For each analysis, save the results to a different object (such as results1, results2 etc) and then ask for the coefficients for example coef(results1).

(Note that you will get the same estimates using glm with family=Gaussian.)

What do you notice about the estimates for each of the regression equations?

Now let's get a slightly more complex output from each results object using e.g. summary(results1).

Where are the coefficients found in the summary output?

What is the same in all of the summary results and what differs?

Now let's take a look at the data visually by running scatterplots for each pair including the "lm" smoother. Notice that "lm" is the same as the "lm" that runs the regression.

Remember that the basic code for scatter plots is: ggplot(dataset, aes(x= , y=)) + geom_point() +geom_smooth(method="lm") + ggtitle("")

Look over your 4 plots with your group.

For which of the 4 plots do you think that the line best fits the data?

In your opinion, which is the plot where the line is the worst fitting for

the data?

Why is it important to do "visual inspection" (that is, look at the plots)

before deciding if a model is accurate?

Now let's look at the fitted values and residuals (also called errors) using the fitted.values() and residuals() functions on the 4 results objects.

Notice that we get a fitted.value and a residual for each observation.

SOC345/lehmansociology documentation built on May 9, 2019, 11:41 a.m.