Which measure indicates the strength and direction of association in a linear regression model?

The regression coefficient, often represented by beta in a linear regression model, is a crucial statistic that indicates both the strength and direction of the relationship between an independent variable and the dependent variable. Specifically, it quantifies how much the dependent variable is expected to increase or decrease when the independent variable increases by one unit, holding all other variables constant.

In the context of linear regression, a positive regression coefficient suggests a positive relationship, meaning as the independent variable increases, the dependent variable also tends to increase. Conversely, a negative regression coefficient indicates an inverse relationship, where an increase in the independent variable is associated with a decrease in the dependent variable. The magnitude of the coefficient also conveys the strength of the association; larger absolute values indicate a stronger effect.

Other statistical measures provided in the choices do not serve this particular function. One-way ANOVA is used to compare means across different groups but does not quantify relationships between variables. The risk ratio pertains to relative risk in epidemiological studies and does not apply to regression modeling. The F-statistic is used to assess the overall significance of the regression model but does not provide information on the strength or direction of individual associations, which is specifically covered by the regression coefficient.