Linear Regression in R | R Linear Regression - r - learn r - r programming
- Regression analysis is a very widely used statistical tool to establish a relationship model between two variables.
- One of these variable is called predictor variable whose value is gathered through experiments.
- The other variable is called response variable whose value is derived from the predictor variable.
- In Linear Regression these two variables are related through an equation, where exponent (power) of both these variables is 1.
- Mathematically a linear relationship represents a straight line when plotted as a graph.
- A non-linear relationship where the exponent of any variable is not equal to 1 creates a curve.
- The general mathematical equation for a linear regression is :
r programming linear regression
y = ax + b
- Following is the description of the parameters used
- y is the response variable.
- x is the predictor variable.
- a and b are constants which are called the coefficients.
Steps to Establish a Regression
- A simple example of regression is predicting weight of a person when his height is known. To do this we need to have the relationship between height and weight of a person. The steps to create the relationship is
- Carry out the experiment of gathering a sample of observed values of height and corresponding weight.
- Create a relationship model using the lm() functions in R.
- Find the coefficients from the model created and create the mathematical equation using these
- Get a summary of the relationship model to know the average error in prediction. Also called residuals.
- To predict the weight of new persons, use the predict() function in R.
Input Data
- Below is the sample data representing the observations
# Values of height 151, 174, 138, 186, 128, 136, 179, 163, 152, 131 # Values of weight. 63, 81, 56, 91, 47, 57, 76, 72, 62, 48
lm() Function
- This function creates the relationship model between the predictor and the response variable.
Syntax
- The basic syntax for lm() function in linear regression is
lm(formula,data)
- Following is the description of the parameters used
- formula is a symbol presenting the relation between x and y.
- data is the vector on which the formula will be applied.
Create Relationship Model & get the Coefficients
x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)
y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)
# Apply the lm() function.
relation <- lm(y~x)
print(relation)- When we execute the above code, it produces the following result
Call: lm(formula = y ~ x) Coefficients: (Intercept) x -38.4551 0.6746
Get the Summary of the Relationship
x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)
y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)
# Apply the lm() function.
relation <- lm(y~x)
print(summary(relation))- When we execute the above code, it produces the following result
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-6.3002 -1.6629 0.0412 1.8944 3.9775
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -38.45509 8.04901 -4.778 0.00139 **
x 0.67461 0.05191 12.997 1.16e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.253 on 8 degrees of freedom
Multiple R-squared: 0.9548, Adjusted R-squared: 0.9491
F-statistic: 168.9 on 1 and 8 DF, p-value: 1.164e-06
predict() Function
Syntax
- The basic syntax for predict() in linear regression is
predict(object, newdata)
- Following is the description of the parameters used
- object is the formula which is already created using the lm() function.
- newdata is the vector containing the new value for predictor variable.
Predict the weight of new persons
# The predictor vector.
x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)
# The resposne vector.
y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)
# Apply the lm() function.
relation <- lm(y~x)
# Find weight of a person with height 170.
a <- data.frame(x = 170)
result <- predict(relation,a)
print(result)
- When we execute the above code, it produces the following result
1 76.22869
Visualize the Regression Graphically
# Create the predictor and response variable.
x <- c(151, 174, 138, 186, 128, 136, 179, 163, 152, 131)
y <- c(63, 81, 56, 91, 47, 57, 76, 72, 62, 48)
relation <- lm(y~x)
# Give the chart file a name.
png(file = "linearregression.png")
# Plot the chart.
plot(y,x,col = "blue",main = "Height & Weight Regression",
abline(lm(x~y)),cex = 1.3,pch = 16,xlab = "Weight in Kg",ylab = "Height in cm")
# Save the file.
dev.off()
- When we execute the above code, it produces the following result
