Which is most likely the correlation coefficient for the set of data shown?

Which is most likely the correlation coefficient for the set of data shown?

December 12, 2024

Question:Which is most likely the correlation coefficient for the set of data shown?

A.–0.83
B.–0.21
C.0.21
D.0.83

Answer: B.–0.21

Explanation:

Step1: Observing the Trend

The scatter plot shows data points that, overall, decrease in value as the x-value increases. This indicates a negative relationship between the variables.

Step2: Assessing the Strength of the Relationship

Although the trend is negative, the points are scattered and do not lie close to a straight line. A strong negative correlation (close to –1) would show points tightly clustered around a downward-sloping line. Here, the spread is relatively large, implying a weak negative correlation.

Step3: Comparing with Given Options

Among the given options:

  • –0.83 indicates a strong negative correlation.
  • –0.21 indicates a weak negative correlation.
  • 0.21 or 0.83 would represent a positive correlation, which does not match the downward trend.

The best fit is the weak negative correlation, which is –0.21.

Extended Knowledge:

Interpreting Correlation Coefficients

  • A correlation coefficient (r) close to ±1 indicates a strong linear relationship.
  • A correlation coefficient (r) close to 0 indicates a weak or no linear relationship.
  • Negative values indicate an inverse relationship; as one variable increases, the other tends to decrease.

Practical Application

Correlation coefficients are widely used in statistics to measure the strength of linear relationships. Understanding whether a relationship is strong or weak helps in making decisions, such as determining whether it’s worth building predictive models or further exploring the relationship.