Final answer:
Of the provided options, the most indicative sign of multicollinearity is High R² and significant F statistic coupled with individually insignificant predictor variables. This indicates that while the model explains variability well, the lack of individual predictors' significance suggests they might have overlapping explanatory power.
Step-by-step explanation:
The detection of multicollinearity in a regression model indicates that two or more predictors are highly linearly related. This makes the coefficients unreliable for interpretation. Among the options provided:
- Individually insignificant predictor variables don't necessarily indicate multicollinearity.
- High R2 plus individually insignificant predictor variables could suggest multicollinearity because the model as a whole explains a significant proportion of the variability, yet no individual predictor stands out.
- High R2 and significant F statistic coupled with insignificant predictor variables is a strong indication of multicollinearity. It shows the model explains variance well, yet none of the predictors individually appear to be contributing, suggesting they may be providing redundant information about the outcome.
- Significant F statistic coupled with individually insignificant predictor variables is similar to the above and could suggest multicollinearity.
Correlation coefficient, represented by r, and the coefficient of determination, r2, are also used in diagnosing multicollinearity. A significant r indicates a strong linear association between variables. However, if r is not significantly different from zero, it is not significant. Checking the change in r after removing potentially multicollinear variables can also be helpful. To summarize, option C: High R2 and significant F statistic coupled with insignificant predictor variables indicate a potential multicollinearity issue.