Question

Select the statements below which are false about scatterplots (you may need to select more than one item).

A) While scatterplots can show the direction of the relationship, they cannot illustrate the strength of a relationship.
B) Scatterplots are effective at picturing the associations between two qualitative variables. | Scatterplots cannot be used to demonstrate non-linear relationships.
C) Scatterplots can picture the strength of a linear relationship between two numerical variables but not the strength of a non-linear relationship between two numerical variables.
D) Scatterplots are useful for determining if two variables are linearly or non- linearly associated.

Answer 1

Statements A, B, and C are false because scatterplots can show the strength of the relationship between variables, are typically used for quantitative data, and can illustrate the strength of both linear and non-linear relationships.

Step-by-step explanation:

The statements about scatterplots that are false can be identified as follows:

• Statement A is false because scatterplots can show both the direction and the strength of the relationship between two numerical variables. A scatterplot with points closely clustered along a specific pattern (linear or otherwise) indicates a strong relationship, while a more dispersed pattern indicates a weaker relationship.
• Statement B is false because scatterplots are typically used for quantitative data, not qualitative. Scatterplots depict the relationship between two numerical variables, not categorical data.
• Statement C is misleading as scatterplots can be used to illustrate the strength of both linear and non-linear relationships. While scatterplots are indeed commonly used to assess the strength of a linear relationship, they can also show non-linear patterns such as quadratic, exponential, or logarithmic relationships.

Statement D is true because scatterplots are useful for determining if two variables are linearly or non-linearly associated. The shape of the pattern formed by the data points can suggest the nature of the relationship.

Answer 2

Scatterplots can illustrate the strength of a relationship, both linear and non-linear, and can determine if two variables are linearly or non-linearly associated.

Step-by-step explanation:

In the given question, we are presented with multiple statements about scatterplots and we are asked to identify the false ones.

A) While scatterplots can show the direction of the relationship, they cannot illustrate the strength of a relationship. This statement is false. Scatterplots can indeed illustrate the strength of a relationship by showing how closely the points cluster together.

C) Scatterplots can picture the strength of a linear relationship between two numerical variables but not the strength of a non-linear relationship between two numerical variables. This statement is also false. Scatterplots can show the strength of both linear and non-linear relationships.

D) Scatterplots are useful for determining if two variables are linearly or non-linearly associated. This statement is true. Scatterplots can provide insights into the nature of the relationship between two variables, whether it is linear or non-linear.

Therefore, the false statements are A) and C).