Residual Plot Calculator calculates residuals for linear regression and visually represents the data through a residual plot. This helps to assess how closely a regression model matches the data and also finds any unusual points or patterns that might affect the model's accuracy.

In a residual plot, the values of a predictor variable are displayed along the x-axis and the residuals are displayed along the y-axis.

## What is the normal residual plot?

A normal residual plot is a type of graph that is used to check the quality of the linear regression. In this, residuals are evaluated based on statistical assumptions such as:

- Constant Variance
- Independent Variable, and
- Normality of the Distribution

A normal __residual plot__ is one where the residuals (differences between predicted and observed values) are randomly scattered around the horizontal axis.

The calculator ensures that these differences are evenly distributed and do not show any specific patterns, and also indicates that the regression model fits the statistical data accurately.

## How to make a residual plot?

**Create Predictions:** Suppose you have a regression model that predicts students' exam scores based on the number of hours they studied. You have to predict scores for each student in your dataset.

**Calculate Residuals:** Find the difference between the predicted scores and the actual exam scores for each student.

Student | Actual Score | Predicted Score | Residual (Actual - Predicted) |
---|---|---|---|

1 | 85 | 80 | 5 |

2 | 92 | 95 | -3 |

3 | 78 | 75 | 3 |

4 | 88 | 90 | -2 |

5 | 95 | 98 | -3 |

**Plot Residuals:** On a graph, put the number of hours studied on the x-axis and the residuals on the y-axis. Each point on the plot represents a student's __residual__.

- For the first student who scored 85, with a predicted score of 80, plot a point at (number of hours, residual) = (X1, 5).
- For the second student who scored 92 with a predicted score of 95, plot a point at (X2, -3) and so on.

**Check for Patterns:** Look at the plot. If the points are randomly scattered around zero, it suggests a good fit. If there's a pattern or trend, it might indicate a problem with the model.

**Evaluate Accuracy:** Analyze the plot to assess how well your regression model fits the data and if there are any __outliers__ affecting accuracy.

Remember, a residual plot is a visual tool to assess the performance of your model and identify areas for improvement.

## How to use the residual plot calculator?

**Insert Values:** Enter the values of the dependent variable (X) and independent variable (Y)

**Start Calculations:** Click to Calculate

**Results:** Get residual plot results along with step-by-step calculations

## Types of the residual plot:

There are several types of residual plots commonly used in regression analysis. These include

**Normal Residual Plot:** Checks if the residuals follow a normal distribution pattern and have a symmetric shape.

**Homoscedasticity Residual Plot:** Examines whether the spread of residuals remains consistent across all levels of the independent variable. A consistent spread suggests homoscedasticity.

**Heteroscedasticity Residual Plot:** Identifies patterns in the spread of residuals, indicating unequal variance across different levels of the independent variable.

**Outliers Residual Plot:** Helps in spotting any data points that significantly deviate from the overall pattern, potentially influencing the regression model.

**Leverage Residual Plot:** Assesses how much each point influences our predictions.

**Partial Residual Plot:** Illustrates the relationship between a specific independent variable and the dependent variable while keeping other variables constant. It helps in understanding the individual impact of each variable.

## How do you know if a residual plot is normal?

To check if a residual plot is normal, observe a symmetrical and bell-shaped pattern in the points that resemble a mound or hill. Additionally, the Residual Histogram is a helpful tool for assessing whether the differences in our data follow a normal distribution.