ANOVA

Print the first 6 rows of the lung capacity data

lung.capacity <- read.csv("C:\\Users\\pranit\\Documents\\Imarticus\\LungCapData.csv")
head(lung.capacity)

##   LungCap Age Height Smoke Gender Caesarean
## 1   6.475   6   62.1    no   male        no
## 2  10.125  18   74.7   yes female        no
## 3   9.550  16   69.7    no female       yes
## 4  11.125  14   71.0    no   male        no
## 5   4.800   5   56.9    no   male        no
## 6   6.225  11   58.7    no female        no

Using ggplot, create a histogram for lungcap variable

library(ggplot2)
ggplot(data = lung.capacity,aes(x = LungCap)) + geom_histogram(color = "red")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Create Boxplot for Lungcap and age

ggplot(lung.capacity, aes(x= LungCap, y = Age )) +  geom_boxplot()

## Warning: Continuous x aesthetic -- did you forget aes(group=...)?

ggplot(lung.capacity, aes(y= LungCap, x = Age )) +  geom_boxplot()

## Warning: Continuous x aesthetic -- did you forget aes(group=...)?

create a barplot for gender variable and print proportion table as well

ggplot(lung.capacity, aes(x = Gender)) + geom_bar()

prop.table(table(lung.capacity$Gender))

## 
##    female      male 
## 0.4937931 0.5062069

create a side by side boxplot for gender and compare the lung capacity of male and female

ggplot(lung.capacity, aes(x= Gender, y =LungCap)) +  geom_boxplot()

## Compare and contrast the gender variable against smoke variable using bar plot

ggplot(lung.capacity,aes(x = Gender,fill = factor(Smoke))) + 
  geom_bar(position = position_dodge(1))

Generate a full linear model with all varaible ,print r squared ,RMSE,

Residual plot

library(caret)

## Loading required package: lattice

library(lattice)
linear <- lm(data = lung.capacity)
z <- summary(linear)
predictions <- predict(linear, lung.capacity[-1])
RMSE(predictions, lung.capacity$LungCap)

## [1] 1.015587

par(mfrow = c(2, 2))
plot(linear)

Generate the reduced linear model with only significant variables, print the same value

reducelm <- lm(data = lung.capacity,lung.capacity$LungCap ~ Age + Height +
                                                     Smoke + Gender)
predictions <- predict(reducelm, lung.capacity[-1])
RMSE(predictions, lung.capacity$LungCap)

## [1] 1.019516

summary(reducelm)

## 
## Call:
## lm(formula = lung.capacity$LungCap ~ Age + Height + Smoke + Gender, 
##     data = lung.capacity)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2915 -0.7360  0.0184  0.7125  3.0599 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -11.33282    0.47245 -23.987  < 2e-16 ***
## Age           0.16012    0.01806   8.864  < 2e-16 ***
## Height        0.26363    0.01009  26.123  < 2e-16 ***
## Smokeyes     -0.61774    0.12633  -4.890 1.24e-06 ***
## Gendermale    0.38528    0.07991   4.822 1.74e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.023 on 720 degrees of freedom
## Multiple R-squared:  0.8531, Adjusted R-squared:  0.8523 
## F-statistic:  1045 on 4 and 720 DF,  p-value: < 2.2e-16

For F - Test (ANOVA) , Write your null and alternative hypothesis

Null Hypothesis: there is no significance difference

Alternative Hypothesis : there is significance differnece

anv <- anova(linear,reducelm,test = "F")

## Warning in anova.lmlist(object, ...): models with response '"lung.capacity
## $LungCap"' removed because response differs from model 1

summary(anv)

##        Df            Sum Sq            Mean Sq           F value        
##  Min.   :  1.0   Min.   :   5.797   Min.   :   1.04   Min.   :   5.574  
##  1st Qu.:  1.0   1st Qu.:  25.164   1st Qu.:  10.43   1st Qu.:  23.396  
##  Median :  1.0   Median : 387.718   Median :  26.00   Median :  26.595  
##  Mean   :120.7   Mean   : 855.079   Mean   : 730.62   Mean   : 842.806  
##  3rd Qu.:  1.0   3rd Qu.: 845.378   3rd Qu.: 665.35   3rd Qu.: 844.125  
##  Max.   :719.0   Max.   :3446.995   Max.   :3446.99   Max.   :3314.339  
##                                                       NA's   :1         
##      Pr(>F)        
##  Min.   :0.00e+00  
##  1st Qu.:0.00e+00  
##  Median :3.00e-07  
##  Mean   :3.70e-03  
##  3rd Qu.:1.60e-06  
##  Max.   :1.85e-02  
##  NA's   :1

anv

## Analysis of Variance Table
## 
## Response: LungCap
##            Df Sum Sq Mean Sq   F value    Pr(>F)    
## Age         1 3447.0  3447.0 3314.3391 < 2.2e-16 ***
## Height      1  877.9   877.9  844.1254 < 2.2e-16 ***
## Smoke       1   27.7    27.7   26.5945 3.248e-07 ***
## Gender      1   24.3    24.3   23.3963 1.614e-06 ***
## Caesarean   1    5.8     5.8    5.5737    0.0185 *  
## Residuals 719  747.8     1.0                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Print F - statistics and write your observations regarding the same

anv$`F value`

## [1] 3314.339117  844.125403   26.594508   23.396293    5.573723          NA