Final answer:
To match the scatter plot with a correlation coefficient, one must recognize the nature of the relationships indicated by positive, negative, and zero correlations. The strength of correlation is determined by its proximity to 1 or -1, with values closer to these extremes indicating stronger relationships and the potential for the line to be used for prediction.
Step-by-step explanation:
The question is asking to match the given scatter plot with one of the provided correlation coefficients. We need to understand the nature of correlations to answer this:
- Positive correlation (0 < r < 1): means that as one variable increases, the other variable also increases.
- Negative correlation (-1 < r < 0): signifies that as one variable increases, the other decreases.
- Zero correlation (r = 0): implies there is no linear relationship between the variables.
A scatter plot with a correlation coefficient of r = 0.95 would show a very strong positive linear relationship between the two variables, as the points would be closely grouped along an upward-sloping line.
A scatter plot with a correlation coefficient of r = -0.89 would show a strong negative linear relationship, with points closely grouped along a downward-sloping line.
Scatter plots with correlation coefficients of r = -0.39 and r = -0.26 would show a weaker negative linear relationship, with more scatter among the points and a less steep downward-sloping trend.
When deciding if a correlation coefficient is significant, you may use a critical values table corresponding to the sample size to find the cutoff points. If the computed correlation is greater than the critical value, it is considered significant and the line can be used for prediction.