Final answer:
Multicollinearity is considered serious if the correlation coefficient exceeds 0.9. A correlation of approximately 0.71 or higher is needed for a coefficient of determination of at least 0.50. The strength of the relationship is indicated by how close the correlation coefficient is to 1 or -1.
Step-by-step explanation:
Multicollinearity will be considered serious if the absolute value of the correlation coefficient between any pair of independent variables exceeds 0.9 (C). However, this threshold is not strict and some sources may consider multicollinearity to be a concern at lower levels such as 0.7 or even 0.5, depending on the context. The coefficient of determination, which is the square of the correlation coefficient, would need to be at least 0.50 to infer a strong linear relationship. This would require a correlation of approximately 0.71 or higher, considering the calculation √0.5 ≈ 0.71. The correlation coefficient indicates the strongest relationship when it is closest to 1 or -1, highlighting a strong positive or negative linear relationship, respectively. Conversely, when the correlation coefficient is closest to 0 it indicates a weak or non-existent relationship. If a tested correlation coefficient is significantly different from zero, we conclude that there is a significant linear relationship present.