Linear Regression Analysis

In this notebook, we will be dealing with scatter plot, correlation analysis, and simple linear regression analysis.

Scatter plot

Scatter plot can be created by using the following code:

plot(datax, datay, main="Title", xlab="xaxis", ylab="yaxis ", pch=19)

Here, pch represents the dot type, and the list of it can be found in the following link:

http://www.sthda.com/english/wiki/r-plot-pch-symbols-the-different-point-shapes-available-in-r

We will illustrate one example here:

df <- read.csv('Data/NHANES.csv')
plot(df$Weight, df$Height, main='Weight vs Height', xlab='Weight', ylab='Height', pch=19)

The overlaps are difficult to see, so we can use a point with a hollow center:

plot(df$Weight, df$Height, main='Weight vs Height', xlab='Weight', ylab='Height', pch=1, col='blue')

Correlation analysis

Correlation coefficient can be simply computed by using the following code:

cor(data1, data2, use = "complete.obs")

use = "complete.obs" means to exclude the missing observations.

cor(df$Weight, df$Height, use = "complete.obs")

## [1] 0.7489522

Since the correlation coefficient is a relatively large number, we can conclude that there is a strong correlation between height and weight.

Simple linear regression analysis

Simple linear regression analysis can be conducted by using the following R code:

summary(lm(datay ~ datax, data = df))

Here, datay represents the y-axis data, datax represents the x-axis data, and df is the name of the dataframe.

summary(lm(Height~Weight, data=df))

## 
## Call:
## lm(formula = Height ~ Weight, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -79.942  -7.064   2.090   9.137  35.019 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.220e+02  3.846e-01   317.2   <2e-16 ***
## Weight      5.482e-01  4.942e-03   110.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.37 on 9632 degrees of freedom
##   (366 observations deleted due to missingness)
## Multiple R-squared:  0.5609, Adjusted R-squared:  0.5609 
## F-statistic: 1.231e+04 on 1 and 9632 DF,  p-value: < 2.2e-16

This shows the intercept, the coefficient and the p-values. People who are interested in learning more about the given information should consult a statistics textbook.

Plot regression line

We can plot a regression line in a scatter plot by using the following code:

abline(lm(datay ~ datax, data = df))

with the scatter plot code:

plot(df$Weight, df$Height, main='Weight vs Height', xlab='Weight', ylab='Height', pch=1, col='blue')
abline(lm(Height~Weight, data=df), col='red')

Multiple Linear Regression Analysis

We can add multiple variables in the linear regression analysis by adding a variable afterwards:

summary(lm(datay ~ datax1 + datax2, data = df))

if there are more than two variables, add + datax3 after + datax2 argument.

summary(lm(Height~Weight+Age, data=df))

## 
## Call:
## lm(formula = Height ~ Weight + Age, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -74.096  -7.441   1.442   8.969  36.975 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.205e+02  3.850e-01  312.90   <2e-16 ***
## Weight      4.990e-01  5.467e-03   91.28   <2e-16 ***
## Age         1.345e-01  6.915e-03   19.46   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.12 on 9631 degrees of freedom
##   (366 observations deleted due to missingness)
## Multiple R-squared:  0.5775, Adjusted R-squared:  0.5774 
## F-statistic:  6583 on 2 and 9631 DF,  p-value: < 2.2e-16

This shows that both weight and age are significant predictors of height.