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Yosef is studying penguin body size allometry. He wants to know if the relations...

Oct 22, 2024

Yosef is studying penguin body size allometry. He wants to know if the relationship between body mass (g) and bill depth (mm) varies by species. He did some exploratory data analysis and ran a model but needs help interpreting the output. Consider the figures below and select the statements that are correct.

Solution by Steps

step 1

To determine if the relationship between body mass (g) and bill depth (mm) varies by species, we can use an analysis of variance (ANOVA) or a regression model that includes an interaction term between species and the predictor variables

step 2

If the model output shows a significant interaction term, it indicates that the relationship between body mass and bill depth differs across species. This can be assessed using the p-value associated with the interaction term in the regression output

step 3

Additionally, visualizations such as scatter plots with regression lines for each species can help illustrate these differences. If the slopes of the lines differ significantly, this supports the conclusion that the relationship varies by species

Answer

The relationship between body mass and bill depth varies by species if the interaction term is significant in the model output.

Key Concept

Interaction effects in regression analysis indicate how the relationship between variables changes across different groups.

Explanation

A significant interaction term suggests that the effect of one variable on the outcome depends on the level of another variable, in this case, species.

Solution by Steps

step 1

To determine if the relationship between body mass and bill length varies by species, we need to assess the interaction between species and bill length in the model output. If the interaction term is significant, it indicates that the relationship is not the same across species

step 2

The scatter plots show different slopes for the lines representing each species, suggesting that the rate of increase in body mass with bill length differs among species. This supports the idea of an interaction effect

step 3

Answer choice A states that body mass increases with bill length for all species, which is true, but it does not address the variation in rates. Answer choice B correctly identifies that Gentoo penguins have larger body mass and longer bills than the other species. Answer choice C incorrectly states that body mass increases at the same rate for all species, which contradicts the observed differences in slopes. Answer choice D correctly suggests that there is an interaction between bill length and species based on the plots

Answer

Key Concept

Interaction effects in regression analysis

Explanation

Interaction effects indicate that the relationship between predictor and response variables differs across levels of another variable, in this case, species.