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

```

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

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

x y1 -0.56047565 -0.99422582 -0.23017749 -1.15482283 1.55870831 2.11788094 0.07050839 0.80041725 0.12928774 -1.41866516 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 squaresoptm_function <- function(data, par) { with(data, sum((par[1] + par[2] * x - y)^2))}

`` Next, we can use theoptim` 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 optimoptim_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 theoptimfunction with those of a conventional linear model provided by thelm` function:

```

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

`` The resulting plot (Figure 1) should show that both theoptimandlmfunctions returned the same result, indicating that our manual optimization using theoptim`.

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