Which of the following are factors adversely influencing interpretation of correlation coefficient?
(1) Sampling Restricted Range
(2) Combining Heterogeneous Subgroups
(3) Presence of Bivariate Outliers
(4) Linearity

Correct option is D

Three factors adversely affect correlation interpretation: (1) Restricted range - limiting the variability in one or both variables artificially reduces the correlation coefficient, (2) Combining heterogeneous subgroups - can create spurious correlations or mask true relationships within subgroups, and (3) Bivariate outliers - extreme values can dramatically inflate or deflate correlation coefficients. However, linearity (4) is not an adverse factor but rather an assumption of Pearson correlation; it becomes problematic only when violated (non-linearity), but linearity itself is desirable.

Information Booster:
1. Range Restriction: Reducing variability attenuates correlation; for example, correlating SAT scores only among admitted students (restricted range) underestimates the true relationship
2. Heterogeneous Groups: Simpson's paradox can occur where correlations differ within subgroups versus the combined sample
3. Outlier Impact: Even one or two extreme bivariate points can substantially change the correlation coefficient
4. Statistical Remedies: Include using full range of scores, analyzing subgroups separately, and using robust correlation methods or removing outliers
5. Interpretation Caution: Always examine scatterplots to identify these problems before interpreting correlation coefficients