Remember to install.package(“AER”), then library(AER).

The Database I am going to use is CASchools which contains information about test scores in the State of California.

The tests are on:

Some the other variables are:

Let’s have a look at the variables contained in the dataset:

summary(CASchools)
##    district            school                  county      grades   
##  Length:420         Length:420         Sonoma     : 29   KK-06: 61  
##  Class :character   Class :character   Kern       : 27   KK-08:359  
##  Mode  :character   Mode  :character   Los Angeles: 27              
##                                        Tulare     : 24              
##                                        San Diego  : 21              
##                                        Santa Clara: 20              
##                                        (Other)    :272              
##     students          teachers          calworks          lunch       
##  Min.   :   81.0   Min.   :   4.85   Min.   : 0.000   Min.   :  0.00  
##  1st Qu.:  379.0   1st Qu.:  19.66   1st Qu.: 4.395   1st Qu.: 23.28  
##  Median :  950.5   Median :  48.56   Median :10.520   Median : 41.75  
##  Mean   : 2628.8   Mean   : 129.07   Mean   :13.246   Mean   : 44.71  
##  3rd Qu.: 3008.0   3rd Qu.: 146.35   3rd Qu.:18.981   3rd Qu.: 66.86  
##  Max.   :27176.0   Max.   :1429.00   Max.   :78.994   Max.   :100.00  
##                                                                       
##     computer       expenditure       income          english      
##  Min.   :   0.0   Min.   :3926   Min.   : 5.335   Min.   : 0.000  
##  1st Qu.:  46.0   1st Qu.:4906   1st Qu.:10.639   1st Qu.: 1.941  
##  Median : 117.5   Median :5215   Median :13.728   Median : 8.778  
##  Mean   : 303.4   Mean   :5312   Mean   :15.317   Mean   :15.768  
##  3rd Qu.: 375.2   3rd Qu.:5601   3rd Qu.:17.629   3rd Qu.:22.970  
##  Max.   :3324.0   Max.   :7712   Max.   :55.328   Max.   :85.540  
##                                                                   
##       read            math      
##  Min.   :604.5   Min.   :605.4  
##  1st Qu.:640.4   1st Qu.:639.4  
##  Median :655.8   Median :652.5  
##  Mean   :655.0   Mean   :653.3  
##  3rd Qu.:668.7   3rd Qu.:665.9  
##  Max.   :704.0   Max.   :709.5  
## 
readmean<-mean(CASchools$read)
mathmean<-mean(CASchools$math)

We can see that the exams are graded apparently go from 600 to 710. On average students got around 654 on both exams. In particular students got on average 653.3426185 on the ‘math’ exam and 654.970477 on the Reading (read) exam.

plot(CASchools$read,CASchools$math, main="Correlation between exam results")

plot(CASchools$read,CASchools$income, main="Is income correlated with the Reading results?")

plot(CASchools$math,CASchools$income, main="Is income correlated with the Math results?")