A _______ is a scatter diagram with the residuals on the vertical axis and the explanatory variable on the horizontal axis.

Question

05-06-2024
Mathematics

High School

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A _______ is a scatter diagram with the residuals on the vertical axis and the explanatory variable on the horizontal axis.

Answer :

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prateek45 prateek45 · Answer 1 · 2025-04-02T12:20:31-04:00

Final answer:

A residual plot is a scatter diagram used to assess the fit of a linear regression model, with residuals on the vertical axis and the explanatory variable on the horizontal axis.

Explanation:

A residual plot is a scatter diagram with the residuals on the vertical axis and the explanatory variable on the horizontal axis. If a researcher is interested in analyzing the relationship between two variables, and particularly in assessing the goodness of fit for a linear regression model, a residual plot can be very helpful. It displays how far data points are from the regression line, which indicates the prediction errors (residuals).

In a scatterplot, the values of two variables are plotted along two axes. This type of plot is useful in identifying the type of relationship between the variables, such as linear or non-linear. If after fitting a regression line to the data in a scatterplot, one wants to investigate the adequacy of the regression model, the residual plot is constructed to reveal any patterns in the residuals.

A residual plot with a random scatter of points suggests that a linear model is appropriate for the data. Conversely, a residual plot with a distinct pattern, such as a curve or systematic arrangement of points, suggests that the linear model may not be appropriate, and that there might be a non-linear relationship between the variables.