Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Which of the following correlation coefficients would indicate the strongest relationship between two variables? A. .58 B. 19 C. -.97 D. -.05

Short Answer

Expert verified
Answer: C. -0.97

Step by step solution

01

Understand correlation coefficients

A correlation coefficient measures the strength and direction of the relationship between two variables. The value of the correlation coefficient ranges from -1 to 1. A value close to 1 indicates a strong positive relationship, a value close to -1 shows a strong negative relationship, while a value near 0 indicates a weak or no relationship between the variables.
02

Identify the strongest correlation coefficient

Since the strongest relationship is either a positive or a negative relationship, we need to find the correlation coefficient with the highest absolute value among the given options. Let's analyze the coefficients: A. .58 -> Moderate positive relationship B. 19 -> Invalid coefficient (the value exceeds the -1 to 1 range) C. -0.97 -> Extremely strong negative relationship D. -0.05 -> Very weak negative relationship Only option B (19) is not a valid correlation coefficient, because it exceeds the valid range (-1 to 1).
03

Compare absolute values

Now, let's compare the absolute values of the remaining coefficients: A. |.58| = 0.58 C. |-.97| = 0.97 D. |-.05| = 0.05 Among all the remaining coefficients, 0.97 (option C) has the highest absolute value, which indicates the strongest relationship between the two variables.
04

Answer the question

Based on the analysis, we can conclude that option C, with a correlation coefficient of -0.97, represents the strongest relationship between two variables among all the given options.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Relationship Between Variables
When we talk about the 'relationship between variables', what we are referring to is how one variable changes in response to another. Imagine you are tracking the amount of time students study and their resulting test scores. If you notice that more study time often corresponds with higher test scores, you're observing a relationship between the two variables.

In statistics, this relationship is quantified using correlation coefficients. These coefficients, which always range between -1 and 1, tell us not only whether there is a relationship but also how strong that relationship is. When we see a correlation coefficient that's close to 1 or -1, it indicates a significant connection between the variables at play.
Strength of Correlation
The magnitude of the correlation coefficient indicates the 'strength of correlation'. A correlation coefficient of -1 or 1 signifies an absolute linear relationship, meaning that the two variables move perfectly in tandem - they increase or decrease exactly in proportion to each other. For instance, a coefficient of 1 means that for every positive increase in one variable, there's a positive increase in the second variable at a consistent rate.

A coefficient closer to 0 means a weaker correlation; the changes in one variable are less consistently matched in the second variable. In our example involving study time and test scores, a coefficient of 0.58 suggests a moderate relationship: as study times increase, test scores tend to increase as well, though not as consistently as they might with a higher coefficient.
Positive and Negative Correlation
Correlation coefficients can be 'positive' or 'negative', indicating the direction of the relationship. A 'positive correlation' means that as one variable increases, the other variable also increases. Conversely, a 'negative correlation' means that as one variable increases, the other decreases.

Take, for example, two scenarios: In one, a coefficient of 0.58 shows that more study time is moderately associated with better test scores (positive correlation). In another situation, a coefficient of -0.97 means that as the number of hours of television watched increases, perhaps students' test scores significantly decrease (negative correlation). Thus, a strong negative correlation like -0.97 in the original exercise suggests a powerful inverse relationship between the two variables under consideration.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

See all solutions

Recommended explanations on Psychology Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free