## Linear Regression

Linear regression is used to explore the relationship between a continuous dependent variable, and one or more continuous and/or categorical explanatory variables. Other statistical methods, such as ANOVA and ANCOVA, are in reality just forms of linear regression.

### Example usage

### Arguments

data | the data as a data frame |

dep | the dependent variable from data, variable must be numeric |

covs | the covariates from data |

factors | the fixed factors from data |

blocks | a list containing vectors of strings that name the predictors that are added to the model. The elements are added to the model according to their order in the list |

refLevels | a list of lists specifying reference levels of the dependent variable and all the factors |

intercept | 'refLevel' (default) or 'grandMean', coding of the intercept. Either creates contrast so that the intercept represents the reference level or the grand mean |

r | TRUE (default) or FALSE, provide the statistical measure R for the models |

r2 | TRUE (default) or FALSE, provide the statistical measure R-squared for the models |

r2Adj | TRUE or FALSE (default), provide the statistical measure adjusted R-squared for the models |

aic | TRUE or FALSE (default), provide Aikaike's Information Criterion (AIC) for the models |

bic | TRUE or FALSE (default), provide Bayesian Information Criterion (BIC) for the models |

rmse | TRUE or FALSE (default), provide RMSE for the models |

modelTest | TRUE (default) or FALSE, provide the model comparison between the models and the NULL model |

anova | TRUE or FALSE (default), provide the omnibus ANOVA test for the predictors |

ci | TRUE or FALSE (default), provide a confidence interval for the model coefficients |

ciWidth | a number between 50 and 99.9 (default: 95) specifying the confidence interval width |

stdEst | TRUE or FALSE (default), provide a standardized estimate for the model coefficients |

ciStdEst | TRUE or FALSE (default), provide a confidence interval for the model coefficient standardized estimates |

ciWidthStdEst | a number between 50 and 99.9 (default: 95) specifying the confidence interval width |

norm | TRUE or FALSE (default), perform a Shapiro-Wilk test on the residuals |

qqPlot | TRUE or FALSE (default), provide a Q-Q plot of residuals |

resPlots | TRUE or FALSE (default), provide residual plots where the dependent variable and each covariate is plotted against the standardized residuals. |

durbin | TRUE or FALSE (default), provide results of the Durbin- Watson test for autocorrelation |

collin | TRUE or FALSE (default), provide VIF and tolerence collinearity statistics |

cooks | TRUE or FALSE (default), provide summary statistics for the Cook's distance |

emMeans | a formula containing the terms to estimate marginal means for, supports up to three variables per term |

ciEmm | TRUE (default) or FALSE, provide a confidence interval for the estimated marginal means |

ciWidthEmm | a number between 50 and 99.9 (default: 95) specifying the confidence interval width for the estimated marginal means |

emmPlots | TRUE (default) or FALSE, provide estimated marginal means plots |

emmTables | TRUE or FALSE (default), provide estimated marginal means tables |

emmWeights | TRUE (default) or FALSE, weigh each cell equally or weigh them according to the cell frequency |

### Returns

A results object containing:

results$modelFit | a table |

results$modelComp | a table |

results$models | an array of groups |

Tables can be converted to data frames with asDF or as.data.frame(). For example:

results$modelFit$asDF

as.data.frame(results$modelFit)

Elements in arrays can be accessed with [[n]]. For example:

results$models[[1]] # accesses the first element