# Linear fit

A linear model describes the relationship between a continuous response variable and the 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.

**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
- Saving variables
- Logistic fit
- Study design
- Method comparison
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 5.60

Published 27-Apr-2020