# optim Function in R

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optim Function in R, we will explore how to apply a general-purpose optimization using the `optim`

function in R programming language.

We will create example data and then demonstrate the usage of the `optim`

function to minimize the residual sum of squares.

**optim Function in R**

First, let’s create the example data we will use for this tutorial:

# Set a random seed for reproducibility set.seed(123) # Create random data x <- rnorm(500) y <- rnorm(500) + 0.7 * x # Combine x and y into a data frame data <- data.frame(x, y) # Print the head of the data head(data)

This code generates a data frame with two numeric variables, `x`

and `y`

.

x y 1 -0.56047565 -0.9942258 2 -0.23017749 -1.1548228 3 1.55870831 2.1178809 4 0.07050839 0.8004172 5 0.12928774 -1.4186651 6 1.71506499 1.1053980

**Example: Applying optim Function in R**

Now, let’s apply the `optim`

function to minimize the residual sum of squares. We will manually create a function for this purpose:

# Manually create a function for residual sum of squares optm_function <- function(data, par) { with(data, sum((par[1] + par[2] * x - y)^2)) }

Next, we can use the `optim`

function as shown below.

The `par`

argument specifies the initial values for the parameters to be optimized over, the `fn`

argument specifies our function, and the `data`

argument specifies our data frame.

We store the output of the `optim`

function in the `optim_output`

object:

# Applying optim optim_output <- optim(par = c(0, 1), fn = optm_function, data = data)

Finally, we can visualize our results in a plot. We will compare the results of the `optim`

function with those of a conventional linear model provided by the `lm`

function:

# Set plot parameters par(mfrow = c(1, 2)) # Plot results of the optim function plot(data$x, data$y, main = "optim Function") abline(optim_output$par[1], optim_output$par[2], col = "red") # Plot results of the lm function plot(data$x, data$y, main = "lm Function") abline(lm(y ~ x, data), col = "green")

The resulting plot (Figure 1) should show that both the `optim`

and `lm`

functions returned the same result, indicating that our manual optimization using the `optim`

.

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