The scatter plot below shows annual rainfall (in mm) on the x axis and the number of plant species recorded at a site on the y axis. Each point is one location, and the points trace out a clear increasing pattern that looks close to a straight line as rainfall rises.
Based on the pattern in the graph, which one of the following statistical methods would be most appropriate to model the relationship between annual rainfall and the number of plant species?
Show Hint
Both rainfall and species number are continuous variables with a straight-line trend, so use linear regression, not a categorical-group test.
Step 1: Identify the type of data.
Both variables here are continuous and numeric: annual rainfall in millimeters and number of plant species as a count. Neither variable is a set of categories or groups.
Step 2: State what the question is actually asking.
The question asks for a method to model the relationship between two continuous variables, meaning we want a way to predict or describe how plant species number changes as rainfall changes, not just to test whether some groups differ.
Step 3: Read the shape of the scatter plot.
The points rise fairly steadily from low values near \(400\) mm of rainfall and \(400\) species up to high values near \(3500\) mm and \(1300\) to \(1500\) species. The spread of points hugs a straight upward path rather than curving sharply or clustering into separate groups.
Step 4: Match the method to the data and the question.
Linear regression is built exactly for this situation: one continuous outcome variable regressed on one continuous predictor variable, fitting a straight line that summarizes the trend and lets us predict species number from rainfall.
Step 5: Rule out the other three methods.
(A) Kruskal-Wallis test: Compares medians across three or more independent groups defined by a categorical variable. There are no such groups here, only two continuous measurements. (B) Student's t-test: Compares the means of two groups. Again, there is no grouping variable, just a continuous rainfall value for each site. (D) Chi-squared test: Tests association between categorical variables using counts in a contingency table, not a relationship between two continuous measurements.
