Example

In this presentation we will learn how to

• plot

• summarize

• estimate a linear regression in R.

Preperation

If this is your first time on R, there are some useful packages you should consider installing

• R commander

  • A gui interface for R that has pulled down windows and is easy to use.
  • To install type “install.packages(”AER“)” at the R prompt with out the “”.

• AER package

  • Contains several econometric packages and datasets from our textbook that we will use.
  • To install type “install.packages(”AER“)”" at the R prompt with out the “”.

Loading data

R can import data from many different data types, but the easiest is the comma-separated textfile or .csv.

I have provided a dataset called Grades.

• This dataset is used to illustrate the idea of regression analysis.
  
• It contains 3 variables, books, attend and grade and has 40 cases.
  
• BOOKS represents the number of books read by students on a statistics course
• ATTEND represents the number of lectures they attended
• GRADE represents their final grade on the course.

download the file here “https://dl.dropboxusercontent.com/u/25290502/Grades.csv”

Then replace the location in the command below.

Grades<- read.csv("C:/Users/Jose/Dropbox/Public/Grades.csv")

SUMMARY OF THE DATA

An easy way to become familiar with the data is to use

summary(Grades)

##      BOOKS       ATTEND         GRADE     
##  Min.   :0   Min.   : 6.0   Min.   :37.0  
##  1st Qu.:1   1st Qu.:10.0   1st Qu.:51.0  
##  Median :2   Median :15.0   Median :60.5  
##  Mean   :2   Mean   :14.1   Mean   :63.5  
##  3rd Qu.:3   3rd Qu.:18.2   3rd Qu.:73.0  
##  Max.   :4   Max.   :20.0   Max.   :97.0

This code gives you the mean, median, and quartile values.

We can also calculate the mean and standard deviation of individual variables

mean(Grades$BOOKS) #Mean number of Books

## [1] 2

sd(Grades$BOOKS) #Standard Deviation of Books

## [1] 1.432

Boxplots (1)

A boxplot is useful to look at the relative distribution of each variable.

boxplot(Grades, col="lightgray")

Plot Y and X

A simple two dimensional plot can tell us a little about the relationship between the variables.

plot(Grades$ATTEND,Grades$GRADE, ylab="Course Grades",xlab="Classes Attended")

Simple Linear Regression

In class, I will show you how to run a regression from R Commander, but here is the command line code for our example

regress.results <- lm(GRADE ~ ATTEND, data = Grades)
summary(regress.results)

## 
## Call:
## lm(formula = GRADE ~ ATTEND, data = Grades)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -27.78 -10.90   2.02  12.43  31.76 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   36.998      8.169    4.53  5.7e-05 ***
## ATTEND         1.883      0.555    3.39   0.0016 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.8 on 38 degrees of freedom
## Multiple R-squared:  0.233,  Adjusted R-squared:  0.212 
## F-statistic: 11.5 on 1 and 38 DF,  p-value: 0.00163

Plot Part 2

We can now graph a line through our scatter plot

plot(Grades$ATTEND,Grades$GRADE, ylab="Course Grades",xlab="Classes Attended")
abline(coef = coef(regress.results))

Multiple Regression

In class, I will show you how to run a regression from R Commander, but here is the command line code for our example

regress.results <- lm(GRADE ~ ATTEND+BOOKS, data = Grades)
summary(regress.results)

## 
## Call:
## lm(formula = GRADE ~ ATTEND + BOOKS, data = Grades)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -20.80 -13.37   0.06   9.17  32.29 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   37.379      7.745    4.83  2.4e-05 ***
## ATTEND         1.283      0.587    2.19    0.035 *  
## BOOKS          4.037      1.753    2.30    0.027 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.1 on 37 degrees of freedom
## Multiple R-squared:  0.329,  Adjusted R-squared:  0.292 
## F-statistic: 9.06 on 2 and 37 DF,  p-value: 0.000628