Final answer:
To determine the strongest and weakest correlations between variables, one must compare the absolute values of the Pearson correlation coefficients in the correlation matrix. The pairs with the highest and lowest absolute values represent the strongest and weakest relationships, respectively.
Step-by-step explanation:
To generate a correlation matrix, one would typically use statistical software to calculate the Pearson correlation coefficients for all variable pairings. The coefficients range from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
After generating the matrix, you compare the absolute values of the correlation coefficients to determine the strength of the relationships. The variable pair with the highest absolute value are the most strongly correlated (either positively or negatively), and the variable pair with the correlation coefficient closest to zero are the least correlated.
Without the exact values from the correlation matrix, I cannot definitively answer which two variables have the strongest and weakest correlations among the options given (X1 and X4, X2 and X3, X3 and X5, X6 and X7, X5 and X6, X7 and X8). However, based on understanding the concept of correlation, one would look for the highest absolute coefficient for the strongest relationship and the lowest for the weakest.