Residual plot for model diagnostic

Simple linear regression is a fundamental tool in statistics and data analysis and it’s crucial to assess the assumptions of the linear regression model. This involves checking for linearity, constant variance (homoscedasticity), independence of errors, and normality of residuals. These diagnostic procedures help ensure that the model is appropriate for the data and that the conclusions drawn from the regression analysis are valid. In addition to these diagnostic checks, it’s also important to consider influential points and outliers that may have a substantial impact on the regression results. In summary, a thorough examination of the model diagnostics is essential for drawing accurate inferences from a simple linear regression model.

Residual plot is an essential tool in statistical analysis. It provides a visual way to assess the goodness of fit of a regression model by examining the residuals, which are the differences between observed and predicted values. Residual plots can help identify patterns or trends in the residuals, such as non-linear relationships or heteroscedasticity. Additionally, they can reveal potential outliers or influential data points that may significantly impact the model’s performance. By examining these plots, analysts can make informed decisions about the appropriateness of the model and the potential need for model refinement.

Codes:

In Python, we can plot the residual plot for the California Housing data as

# Plot actual vs predicted values
plot(test_data$median_house_value, predictions,
     xlab = "Actual Median House Value",
     ylab = "Predicted Median House Value",
     main = "Actual vs Predicted House Values")
abline(0, 1, col = "red")

In R, for the mtcars dataset, we can plot the residual plot using

# Plot actual vs predicted values
plot(test_data$median_house_value, predictions,
     xlab = "Actual Median House Value",
     ylab = "Predicted Median House Value",
     main = "Actual vs Predicted House Values")
abline(0, 1, col = "red")