Assignment 12 (Discussion):

Load Packages

library(corrplot)
library(dplyr)
library(knitr)

Problem Statement

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

Solution

The data i choose is the heart data from UCI machine learning reprository https://archive.ics.uci.edu/ml/index.php

Read Data

heart <- read.csv("https://archive.ics.uci.edu/ml/machine-learning-databases/heart-disease/processed.cleveland.data",header=FALSE,sep=",",na.strings = '?')
colnames(heart) <- c( "age", "sex", "cp", "trestbps", "chol","fbs", "restecg","thalach","exang", "oldpeak","slope", "ca", "thal", "outcome")

heart<- heart[complete.cases(heart),] #Store only Data without missing value

correlation plot

data_frame <- heart %>% select(age,trestbps,chol,thalach,oldpeak)
M <- cor(data_frame)

col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))
corrplot(M, method="color", col=col(200),  
         type="upper", order="hclust", 
         addCoef.col = "black", # Add coefficient of correlation
         tl.col="black", tl.srt=45, #Text label color and rotation
         # Combine with significance
          insig = "blank", 
         # hide correlation coefficient on the principal diagonal
         diag=FALSE 
)

Multiple Linear Regression:

#lm(formula = Y(dependent) ~ X1(independent) + X2 + X3 + ..., data=table_name_optional)
  
attach(heart)

MLR <- lm(formula = age ~ trestbps + chol + thalach + oldpeak, data=heart)

summary(MLR) #compelete summary of the regression analysis

## 
## Call:
## lm(formula = age ~ trestbps + chol + thalach + oldpeak, data = heart)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -19.5862  -5.6714   0.2889   5.8933  23.5759 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 52.873743   5.026193  10.520  < 2e-16 ***
## trestbps     0.126013   0.026385   4.776 2.83e-06 ***
## chol         0.029522   0.008853   3.335 0.000964 ***
## thalach     -0.149234   0.021216  -7.034 1.43e-11 ***
## oldpeak      0.091232   0.424752   0.215 0.830082    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.85 on 292 degrees of freedom
## Multiple R-squared:  0.2578, Adjusted R-squared:  0.2476 
## F-statistic: 25.36 on 4 and 292 DF,  p-value: < 2.2e-16

confint(MLR)

##                   2.5 %      97.5 %
## (Intercept) 42.98158533 62.76589970
## trestbps     0.07408423  0.17794128
## chol         0.01209884  0.04694573
## thalach     -0.19098955 -0.10747933
## oldpeak     -0.74473150  0.92719518

Residual analysis

plot(fitted(MLR), resid(MLR))

qqnorm((resid(MLR)))
qqline((resid(MLR)))

Based on the residual analysis, I would conclude that the linear model is appropriate. From the plots you can see that the points follow a straight line. This tells us that the residuals are normally distributed.