Question

mary texas cities have experienced substantial growth in population over the last 20 years. the growth of houston, texas, since 2015 is shown in the scatterplot. a least - squares equation that relates the number of years since 2015 to the population of that year (in millions) is given by
population = 0.025( year )+2.01.
based on the residual plot, is a linear model suitable for modeling the population growth of houston?
a linear model is suitable because a pattern is evident in the residual plot.
a linear model is not suitable because the residuals do not cluster around zero.
a linear model is not suitable because the residual plot shows a curved pattern.
a linear model is suitable because the residuals seem to be randomly scattered.

Explanation:

A linear model is suitable if the residuals (the differences between the observed and predicted values) are randomly scattered. If there is a pattern (like a curved pattern) in the residual plot, it indicates that a linear model is not appropriate as it fails to capture the relationship accurately. In this case, we need to check the key concept of residual plots for linear model suitability.

Answer:

A linear model is not suitable because the residual plot shows a curved pattern.