Simple histogram and  Standardized Residual plot

Concepts:

To compute the standardised residual, subtract the anticipated value from the observed value, then divide the result by the estimate’s standard error. The accuracy of predicting the dependent variable from the independent variable is measured by the standard error of the estimate....

Steps to be followed:

Load the required R packages, such as ‘car'(companion to applied regression) and ‘ggplot2’, which include the tools for generating consistent residuals and rendering them. R’s ‘lm()’ function can be used to fit a regression model. Utilize the ‘rstandard()’ function from the ‘car’ package to determine the standardised residuals. To spot probable outliers, visualise the standardised residuals using a scatterplot or a histogram. To comprehend the link between the dependent and independent variables, interpret the standardised residuals....

Using the ‘plot( )’ and ‘plot.lm( )’ functions, you can draw the ‘simple plot’ and ‘standardised residual plot’, respectively in R. Here is an illustration:

R #Create some arbitrary data x <- rnorm(50) y <- 2*x + rnorm(50)   # Create a model of linear regression model <- lm(y ~ x)   # Plotting the simple plot plot(x, y, main = "Simple Plot")   # Plotting the standardized residue plot plot(model, which = 1, main = "Standardized Residue Plot")...

Output:

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Simple histogram and  Standardized Residual plot :

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Output:

R # Generate some random data x <- rnorm(50) y <- 2*x + rnorm(50)   # Fit a linear regression model model <- lm(y ~ x)   # Plot the simple histogram hist(y, main = "Simple Histogram")   # Plot the standardized residual plot plot(model, which = 1, main = "Standardized Residue Plot")...

Here are some  scatter plot examples using R:

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Output:

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Output:

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Output:

A straightforward scatter diagram with a regression line:...

Another example utilising a simulated dataset is as follows:

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output:

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Mathematical Concepts  Used Here:

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