Answer:
Step-by-step explanation:
Correlation between two variables does not necessarily imply a large magnitude of effect in a bivariate regression, and there are several reasons for this:
Correlation does not imply causation: Even if two variables are correlated, it doesn't establish a cause-and-effect relationship between them. Correlation only measures the strength and direction of a linear relationship.
Magnitude of effect depends on units: The scale or units in which variables are measured can greatly influence the magnitude of the correlation. In regression, the size of coefficients is affected by the scale of the variables. Rescaling variables may change the magnitude of the effect without altering the correlation.
Influence of outliers: Outliers can strongly affect correlation but might not have as pronounced an impact on regression coefficients. Regression analysis can provide more robust estimates of the relationship between variables, especially if outliers are handled appropriately.
Direction of the relationship: Correlation only measures the strength and direction (positive or negative) of the linear relationship, but it doesn't provide information about the size of the effect. A correlation of 0.8 could represent a weak or a strong relationship, depending on the context.
Suppression or confounding effects: In some cases, a third variable may influence the relationship between X and Y, creating a suppression or confounding effect. Regression analysis allows for the control of additional variables, providing a more nuanced understanding of the relationship.
In summary, while correlation provides information about the strength and direction of a linear relationship, it does not guarantee a large magnitude of effect in a bivariate regression. The use of regression analysis allows for a more detailed examination of the relationship between variables, taking into account potential confounding factors and providing a clearer understanding of the magnitude of the effect of X on Y.
