Question

Which of the following statements is not true about scatterplots?

a. We don't need scatterplots; we can get the information we need from means, medians, and standard deviations
b. Once we can measure things, we can better manage them
c. Scatterplots show the relationship between two variables
d. In a scatterplot, a single dot represents the values of the two variables we're looking at for a single observation

Answer 1

A scatterplot accurately shows a single observation at the intersection of two variable values, one on the x-axis and one on the y-axis. The pattern of the plot determines if linear regression is suitable, and tools like calculators can help find the regression line while also indicating if a curve model would be more appropriate.

Step-by-step explanation:

In a scatterplot, each dot indeed represents a single observation with its values for two variables: one on the x-axis (independent variable) and one on the y-axis (dependent variable). However, the statement that this is not true about scatterplots is incorrect; it actually describes precisely what a scatterplot is. When analyzing a scatterplot, you look at the pattern of dots to determine the kind of relationship between the two variables. If the variables appear to have a linear relationship, they might be suitable for linear regression. Nevertheless, if the pattern suggests a curve, a linear model might not be appropriate, and a curve model should be considered instead.

Using a calculator to construct a scatterplot helps visualize the relationship between two properties of a system. Regression functions on calculators can then be used to find the least-squares regression line. Still, it's crucial to visually assess the scatterplot to decide whether this linear model is fitting or if another type of model would better represent the data's pattern.