What seems most likely regarding the relation between X and Y given the following scatterplot?

Question

BlackTom AI · Accepted Answer

The question asks what seems most likely about the relation between X and Y based on the given scatterplot, but the answer options are not provided in the prompt.

If we accept the provided answer statement as the intended correct idea: 'If there are 3 groups and Y would have different means in these groups, X and Y might very well have a strong positive correlation overall within each group.' This reflects a common scenario in scatterplots where an overall weak or moderate correlation can disguise a strong within-group relationship due to confounding by a grouping variable.

Explanation step by step:
- Concept: Correlation measures how X and Y move together. A positive correlation means that as X increases, Y tends to increase as well.
- Group structure: If the data are divided into three distinct groups, and each group has a different mean level of Y (and possibly different ranges of X), the overall (pooled) scatterplot can show a weak or non-existent correlation even when each group individually shows a strong positive relationship.
- Within-group interpretation: Within any single group, the points may align closely along an upward trend, yielding a strong positive correlation when restricted to that group.
- Across-group interpretation: If the three groups have different Y means due to a third variable or group effect, combining them can flatten the overall trend, because increases in X may be associated with different baseline Y levels across groups.
- Therefore, it is plausible that there is a strong positive correlation within each group, while the overall correlation across all data could be weaker or misleading if the group differences are not accounted for.

Potential misconceptions to watch for:
- Assuming that a strong overall correlation implies a strong within-group correlation: the opposite can be true if a confounding grouping variable drives the apparent association.
- Ignoring the role of groups: failing to stratify by the 3 groups could lead to incorrect conclusions about the relationship between X and Y.

Limitations: Without the actual scatterplot visual, this reasoning relies on the described scenario (three groups with different Y means). If the plot shows no clear within-group pattern or if X and Y are truly independent within each group, then the statement would be inaccurate.

PSYCH 3321 SP2025 (28481) Homework 8 - due 2/28

What seems most likely regarding the relation between X and Y given the following scatterplot?

查看解析

登录即可查看完整答案

类似问题

TB MC Qu. 10-18 Which of the following potential... Which of the following potential observations are scatter plots used to exhibit?

If 2 items are close to negatively correlated, then the value of the correlation is approximately ..

Which of the following correctly concludes the hypothesis test conducted in the r output above?

Which of the following methods should be used to determine if there is an association between weekly time spent doing homework (in hours) and exam score (in points)?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单