# Linear fit

A linear model describes the relationship between a continuous response variable and one or more explanatory variables using a linear function.

**Simple regression models**

Simple regression models describe the relationship between a single predictor variable and a response variable.**Advanced models**

Advanced models describe the relationship between a response variable and multiple predictor terms.**Scatter plot**

A scatter plot shows the relationship between variables.**Summary of fit**

R² and similar statistics measure how much variability is explained by the model.**Parameter estimates**

Parameter estimates (also called coefficients) are the change in the response associated with a one-unit change of the predictor, all other predictors being held constant.**Effect of model hypothesis test**

An F-test formally tests the hypothesis of whether the model fits the data better than no model.**Predicted against actual Y plot**

A predicted against actual plot shows the effect of the model and compares it against the null model.**Lack of Fit**

An F-test or X^{2}-test formally tests how well the model fits the data.**Effect of terms hypothesis test**

An F-test formally tests whether a term contributes to the model.**Effect leverage plot**

An effect leverage plot, also known as added variable plot or partial regression leverage plot, shows the unique effect of a term in the model.**Effect means**

Effect means are least-squares estimates predicted by the model for each combination of levels in a categorical term, adjusted for the other model effects.**Multiple comparisons**

Multiple comparisons make simultaneous inferences about a set of parameters.**Residual plot**

A residual plot shows the difference between the observed response and the fitted response values.**Residuals - normality**

Normality is the assumption that the underlying residuals are normally distributed, or approximately so.**Residuals - independence**

Autocorrelation occurs when the residuals are not independent of each other. That is, when the value of e[i+1] is not independent from e[i].**Outlier and influence plot**

An influence plot shows the outlyingness, leverage, and influence of each case.**Prediction**

Prediction is the use of the model to predict the population mean or value of an individual future observation, at specific values of the predictors. Inverse prediction deals with the problem of predicting the value of a predictor for a given value of the response variable.

**Available in Analyse-it Editions**

Standard edition

Method Validation edition

Quality Control & Improvement edition

Ultimate edition

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Linear fit
- Simple regression models
- Fitting a simple linear regression
- Advanced models
- Fitting a multiple linear regression
- Performing ANOVA
- Performing 2-way or higher factorial ANOVA
- Performing ANCOVA
- Fitting an advanced linear model
- Scatter plot
- Summary of fit
- Parameter estimates
- Effect of model hypothesis test
- ANOVA table
- Predicted against actual Y plot
- Lack of Fit
- Effect of terms hypothesis test
- Effect leverage plot
- Effect means
- Plotting main effects and interactions
- Multiple comparisons
- Multiple comparison procedures
- Comparing effect means
- Residual plot
- Residuals - normality
- Residuals - independence
- Plotting residuals
- Outlier and influence plot
- Identifying outliers and other influential points
- Prediction
- Making predictions
- Making inverse predictions
- Saving variables
- Logistic / Probit fit
- Study design
- Method comparison / Agreement
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.15

Published 18-Apr-2023