Answer :
Final answer:
The statement 'There is no relationship between scatter diagrams and correlation coefficients' is not true of a scatter diagram; scatter diagrams portray the relationship and correlation between two metric variables, and correlation coefficients can be derived from the pattern of the points in a scatter plot.
Explanation:
The correct answer to the student's question, 'Which of the following is NOT true of a scatter diagram?' is option E) 'There is no relationship between scatter diagrams and correlation coefficients.' This statement is incorrect because scatter diagrams do in fact have a relationship with correlation coefficients. A scatter diagram, or scatter plot, is a type of graph that is used in statistics to display the relationship between two metric variables. It involves plotting data pairs on an x- and y-axis graph to visualize any potential correlation.
Let's address the claims made in the options:
- It is true that a scatter diagram plots data pairs on an x- and y-axis graph (A).
- It correctly portrays the amount of covariation between two metric variables (B).
- It represents each matched pair of x and y variables as points on the graph (C).
- Indeed, when there is no apparent association or relationship, the points fail to form any identifiable pattern (D).
However, scatter diagrams are related to correlation coefficients because the pattern of the points can indicate the strength and direction of the relationship between the variables. Moreover, understanding the scatter plot pattern is crucial when deciding if a linear model is appropriate or if alternative methods to model the data should be considered.
