Interpreting the Model

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How To... > Work with Statistical Objects > Build a Linear Model > Multiple Regression > Interpreting the Model

There’s a lot going on here! There are two things to focus on before we go into the details: There is now a regression equation with three terms that can be used to predict costph from seats and speed. Also, the bar shows that 80% of the variation is accounted for by the linear relationship.

Coefficient

The constant term and the coefficients for the two linear terms. These are also in the regression equation.

Std Error

These numbers are the standard deviation of the sampling distribution of each of the corresponding coefficients.

t-Statistic

The value of student’s t for the coefficient.

p-Value

The probability that a value for the coefficient this different from zero would be obtained if the population value of the coefficient were zero.

ΔR2

The change in R2 that this attribute would contribute if it were the last attribute added (i.e., at the bottom of the list).

Regression Equation

The equation with which you can predict the response. The “hat” over the response attribute name indicates that it is a predicted value.

Ribbon Chart

The bar represents the variation in the response. Each segment of the ribbon represents the portion of that variation “accounted” for by an attribute. The blank segment represents the remaining, unaccounted for, variation.

ANOVA Table

One important number in this table is the p-Value. If this value is small (and a value of zero means that it’s really small), then it is unlikely that the amount of explanation provided by the model would occur by chance under conditions in which there was no linear relationship among the attributes.

R-Squared

This is the total R2 value for the model. You can think of it as the proportion of variation in the response accounted for by the model.