In regression analysis, which statistic reflects the strength of the relationship between the predictors and the dependent variable?

In regression analysis, which statistic reflects the strength of the relationship between the predictors and the dependent variable?

• A. R (the multiple correlation coefficient)
• B. t-statistic
• C. chi-square
• D. z-score

Answer: (A)

The strength of the linear relationship between the predictors and the dependent variable is captured by the multiple correlation coefficient, R. This statistic reflects how well, overall, the predictors relate to the outcome in a linear way—the closer R is to 1, the stronger the relationship, with predicted values matching observed values more closely. R is often accompanied by R^2, the coefficient of determination, which tells what proportion of the variance in the dependent variable is explained by the predictors (for example, an R of 0.8 gives R^2 = 0.64, meaning 64% of the variance is explained). The other statistics have different roles: the t-statistic tests whether a specific predictor’s coefficient is significantly different from zero; chi-square is used for categorical data and tests of independence or goodness of fit; the z-score standardizes a value for comparison. So for describing the overall strength of the relationship between the set of predictors and the outcome, the multiple correlation coefficient, R, is the best descriptor.

The strength of the linear relationship between the predictors and the dependent variable is captured by the multiple correlation coefficient, R. This statistic reflects how well, overall, the predictors relate to the outcome in a linear way—the closer R is to 1, the stronger the relationship, with predicted values matching observed values more closely. R is often accompanied by R^2, the coefficient of determination, which tells what proportion of the variance in the dependent variable is explained by the predictors (for example, an R of 0.8 gives R^2 = 0.64, meaning 64% of the variance is explained).

The other statistics have different roles: the t-statistic tests whether a specific predictor’s coefficient is significantly different from zero; chi-square is used for categorical data and tests of independence or goodness of fit; the z-score standardizes a value for comparison. So for describing the overall strength of the relationship between the set of predictors and the outcome, the multiple correlation coefficient, R, is the best descriptor.