discussionwk11

DATA 605 Discussion week 11

Using R, build a regression model for data that interests you. Conduct residual analysis. Was the linear model appropriate? Why or why not?

Iris Data

head(iris)

##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa

summary(iris)

##   Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
##  Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  
##  1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  
##  Median :5.800   Median :3.000   Median :4.350   Median :1.300  
##  Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  
##  3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  
##  Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  
##        Species  
##  setosa    :50  
##  versicolor:50  
##  virginica :50  
##                 
##                 
## 

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 3.3.3

ggplot(data = iris, aes(x=Sepal.Length, y=Sepal.Width)) + geom_point(size = 2, alpha = .4) + geom_smooth(method = "lm", se = FALSE)

#correlation:
cor(iris$Sepal.Length,iris$Sepal.Width)

## [1] -0.1175698

# linear model
Linear =lm(Sepal.Length~ Sepal.Width, data = iris)

summary(Linear)

## 
## Call:
## lm(formula = Sepal.Length ~ Sepal.Width, data = iris)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5561 -0.6333 -0.1120  0.5579  2.2226 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   6.5262     0.4789   13.63   <2e-16 ***
## Sepal.Width  -0.2234     0.1551   -1.44    0.152    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8251 on 148 degrees of freedom
## Multiple R-squared:  0.01382,    Adjusted R-squared:  0.007159 
## F-statistic: 2.074 on 1 and 148 DF,  p-value: 0.1519

# scatterplot with least squares line
plot(iris$Sepal.Length~iris$Sepal.Width)
abline(Linear)

# residuals plot with constant variability
plot(Linear$residuals ~ iris$Sepal.Length)
abline(h = 0, lty = 3)

# histogram of residuals
hist(Linear$residuals)

# qqplot
qqnorm(Linear$residuals)
qqline(Linear$residuals)

histogram of residual plot appear to be normally distributed