Business Analytics (MGT 4050)

Homework 1 (Introduction to R)

Task 1- Import data and initial exploration

1.1: Import Data

setwd("~/Downloads/Rscript Rstudio projects/Rscript Homework")
setwd("~/Downloads")
df <- read.csv("BostonHousing.csv")

###1.2: Add first 10 rows

head(df,10)

##       crim   zn indus chas   nox    rm   age    dis rad tax ptratio lstat medv
## 1  0.00632 18.0  2.31    0 0.538 6.575  65.2 4.0900   1 296    15.3  4.98 24.0
## 2  0.02731  0.0  7.07    0 0.469 6.421  78.9 4.9671   2 242    17.8  9.14 21.6
## 3  0.02729  0.0  7.07    0 0.469 7.185  61.1 4.9671   2 242    17.8  4.03 34.7
## 4  0.03237  0.0  2.18    0 0.458 6.998  45.8 6.0622   3 222    18.7  2.94 33.4
## 5  0.06905  0.0  2.18    0 0.458 7.147  54.2 6.0622   3 222    18.7  5.33 36.2
## 6  0.02985  0.0  2.18    0 0.458 6.430  58.7 6.0622   3 222    18.7  5.21 28.7
## 7  0.08829 12.5  7.87    0 0.524 6.012  66.6 5.5605   5 311    15.2 12.43 22.9
## 8  0.14455 12.5  7.87    0 0.524 6.172  96.1 5.9505   5 311    15.2 19.15 27.1
## 9  0.21124 12.5  7.87    0 0.524 5.631 100.0 6.0821   5 311    15.2 29.93 16.5
## 10 0.17004 12.5  7.87    0 0.524 6.004  85.9 6.5921   5 311    15.2 17.10 18.9

###1.3: Summary of all variables

summary(df)

##       crim                zn             indus            chas        
##  Min.   : 0.00632   Min.   :  0.00   Min.   : 0.46   Min.   :0.00000  
##  1st Qu.: 0.08205   1st Qu.:  0.00   1st Qu.: 5.19   1st Qu.:0.00000  
##  Median : 0.25651   Median :  0.00   Median : 9.69   Median :0.00000  
##  Mean   : 3.61352   Mean   : 11.36   Mean   :11.14   Mean   :0.06917  
##  3rd Qu.: 3.67708   3rd Qu.: 12.50   3rd Qu.:18.10   3rd Qu.:0.00000  
##  Max.   :88.97620   Max.   :100.00   Max.   :27.74   Max.   :1.00000  
##       nox               rm             age              dis        
##  Min.   :0.3850   Min.   :3.561   Min.   :  2.90   Min.   : 1.130  
##  1st Qu.:0.4490   1st Qu.:5.886   1st Qu.: 45.02   1st Qu.: 2.100  
##  Median :0.5380   Median :6.208   Median : 77.50   Median : 3.207  
##  Mean   :0.5547   Mean   :6.285   Mean   : 68.57   Mean   : 3.795  
##  3rd Qu.:0.6240   3rd Qu.:6.623   3rd Qu.: 94.08   3rd Qu.: 5.188  
##  Max.   :0.8710   Max.   :8.780   Max.   :100.00   Max.   :12.127  
##       rad              tax           ptratio          lstat      
##  Min.   : 1.000   Min.   :187.0   Min.   :12.60   Min.   : 1.73  
##  1st Qu.: 4.000   1st Qu.:279.0   1st Qu.:17.40   1st Qu.: 6.95  
##  Median : 5.000   Median :330.0   Median :19.05   Median :11.36  
##  Mean   : 9.549   Mean   :408.2   Mean   :18.46   Mean   :12.65  
##  3rd Qu.:24.000   3rd Qu.:666.0   3rd Qu.:20.20   3rd Qu.:16.95  
##  Max.   :24.000   Max.   :711.0   Max.   :22.00   Max.   :37.97  
##       medv      
##  Min.   : 5.00  
##  1st Qu.:17.02  
##  Median :21.20  
##  Mean   :22.53  
##  3rd Qu.:25.00  
##  Max.   :50.00

###1.4: Mean value

mean_medv <- mean(df$medv) 
mean_medv

## [1] 22.53281

###1.5: Histogram of Medv Variable, mark the mean val of medv by adding a vertical line

hist(df$medv,
  main= "Histogram of MEDV Aka Median Home Value",
  xlab= "medv($1,000s)",
  border = "blue")
abline(v= mean_medv, col= "red", lwd=2, lty=2)
legend("topright",legend=paste0("Mean=", round(mean_medv, 2)),
      lty = 2, lwd = 2, col="red", bty = "y")

Task 2- Create a variable

###2.6: cat.medv confirmation thing

df$cat.medv <- as.integer(df$medv > 30)

###2.7: calculate the mean of cat.medv + explain what it means

mean_cat_medv <- mean(df$cat.medv, na.rm=TRUE)
mean_cat_medv

## [1] 0.1660079

cat("After getting the mean of the home prices of medv that is over $30,000, which is ", mean_cat_medv,
    " This means ", round(mean_cat_medv*100,2), "% of the census tracts have median home values above $30,000.\n")

## After getting the mean of the home prices of medv that is over $30,000, which is  0.1660079  This means  16.6 % of the census tracts have median home values above $30,000.

Task 3- Bar Chart

###3.8: Calculate the mean of cat.medv for the tracts that bound the Charles River (chas==1) and save it to a variable

m_chas1 <- mean(df$cat.medv[df$chas==1], na.rm = TRUE)
m_chas1

## [1] 0.3142857

###3.9 Mean of cat.medv for tracts that do not bound the river (chas==0)

m_chas0 <- mean(df$cat.medv[df$chas== 0], no.rm = TRUE)
m_chas0

## [1] 0.1549894

###3.10 Create a vector of the two means

comb_chas <-c(m_chas1, m_chas0)
comb_chas

## [1] 0.3142857 0.1549894

###3.11 Plot a bar chart

bc <- barplot(comb_chas,
    names.arg = c("chas = 1 (Bounds River)", "chas = 0 (Does Not Bound)"),
    ylim=c(0,1),
    ylab="proportion with MEDV>30k",
    main = "Chart of Tracts with MEDV > $30k by the Charles River Boundary",
    border= "black")
text(x = bc, y = comb_chas, labels = round(comb_chas, 3), pos = 3)

###3.12 What I can tell from the bar chart

cat("From the bar chart I can tell that there are more Tracts that bound the charles river from homes that are worth more than $30,000. 31% of homes that border the Charles river are worth over $30,000 usd bound the river while only 15.5% of homes that dont border it, are worth over $30,000 usd")

## From the bar chart I can tell that there are more Tracts that bound the charles river from homes that are worth more than $30,000. 31% of homes that border the Charles river are worth over $30,000 usd bound the river while only 15.5% of homes that dont border it, are worth over $30,000 usd

Task 4: Boxplot

###4.13 side by side boxplot

boxplot(medv ~ as.factor(chas), data = df,
        names = c("chas = 0 (No)", "chas = 1 (Yes)"),
        xlab = "Tract bounds Charles River?",
        ylab = "MEDV ($1,000s)",
        main = "MEDV by Charles River")

Task 5: Scatter Plot

###5.14 Scatter plot of medv
plot(df$lstat, df$medv,
     xlab = "lstat (% lower socioeconomic status)",
     ylab = "medv ($1,000s)",
     main = "Scatterplot of MEDV vs LSTAT",
     pch = 19, 
     cex = 0.7, 
     col = "black")
     
###5.15 Linear Regression

fit <- lm(medv ~ lstat, data = df)
summary(fit)

## 
## Call:
## lm(formula = medv ~ lstat, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.168  -3.990  -1.318   2.034  24.500 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 34.55384    0.56263   61.41   <2e-16 ***
## lstat       -0.95005    0.03873  -24.53   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.216 on 504 degrees of freedom
## Multiple R-squared:  0.5441, Adjusted R-squared:  0.5432 
## F-statistic: 601.6 on 1 and 504 DF,  p-value: < 2.2e-16

###5.16 Line + Legend

abline(fit, col = "blue", lwd = 2)
legend("topright", legend = "Fitted line: medv ~ lstat",
       col = "blue", lwd = 2, bty = "n")