The angle between the two regression lines indicates the strength of the correlation. If the lines are closer together (smaller angle), the correlation is stronger. If they are farther apart (larger angle), the correlation is weaker, indicating a lower degree of linear relationship between the variables.

The question asks for a strong inverse relationship, which mathematically requires a negative coefficient close to -1.0. While -0.80 is the correct statistical representation of a strong inverse relationship, the provided answer key is A (0.80). This suggests a potential error in the source key, as 0.80 indicates a strong positive correlation, not an inverse one.

A correlation coefficient (r) ranges from -1 to +1. A value of +1 indicates a perfect positive linear relationship, while a value of -1 indicates a perfect negative linear relationship. Both represent perfect correlation, as the data points would fall exactly on a straight line.

Regression coefficients are independent of the change of origin but are dependent on the change of scale. Therefore, stating they are independent of both is incorrect. The other statements are standard properties of correlation and regression analysis.

A correlation coefficient ranges from -1 to +1. An inverse (negative) relationship means that as one variable increases, the other decreases. A value of -0.80 indicates a strong negative correlation, which aligns with the statement that higher weight is associated with lower life expectancy.

The Pearson correlation coefficient specifically measures the strength and direction of a linear relationship between two continuous variables. It does not measure non-linear associations, which would require other statistical methods like Spearman's rank correlation or non-linear regression models. Thus, only statement 1 is accurate.

Both statements are factually accurate in the context of classical linear regression. However, the reason provided describes the functional purpose of regression (prediction/estimation) rather than explaining why the independent variables are treated as fixed quantities. Thus, while both are true, the reason does not explain the assertion.

A relationship represented by a curve is technically a nonlinear relationship. However, the provided answer key identifies this as 'Linear relationship'. This is a contradiction in terminology, as linear relationships are defined by straight lines. We preserve the answer key as instructed while noting the conceptual discrepancy.

The Pearson correlation coefficient (r) is calculated as Σxy / (n * σx * σy). If the sum of the product of deviations (Σxy) is zero, the numerator becomes zero, resulting in a correlation coefficient of zero. This indicates that there is no linear relationship between the two variables, meaning they are uncorrelated.

Correlation measures the degree of association between two variables. In finance, it is a critical concept for portfolio management because it helps investors understand how different assets interact. When assets have low or negative correlation, combining them in a portfolio can reduce overall risk without necessarily sacrificing expected returns, as the price movements of the assets tend to offset each other.