In this tutorial, we want to model the relationship between the cars consumption and their weight, engine-size and horsepower. We describe the outputs of Tanagra by associating them with the used formulas. We highlight the importance of the unscaled covariance matrix of the estimated coefficients [(X'X)-1] (Tanagra 1.4.38 and later). It is used for the subsequent analysis: individual significance of coefficients, simultaneous significance of several coefficients, testing linear combinations of coefficients, computation of the standard error for the prediction interval. These analyses are performed into the Excel spreadsheet.

Thereafter, we perform the same analyses with the R software. We identify the objects provided by the lm(.) procedure that we can use in the same context.

**Keywords**: linear regression, multiple regression, R software, lm, summary.lm, testing significance, prediction interval

**Components**: MULTIPLE LINEAR REGRESSION

**Tutorial**: en_Tanagra_Multiple_Regression_Results.pdf

**Dataset**: cars_consumption.zip

**References**:

D. Garson, "Multiple Regression"