The scatterplot below shows the percentage of the US population that is foreign born for the years 1910 - 1990.For what range of years is a linear model appropriate?
A)One linear model is appropriate for the years 1910 through 1950 and another linear model for the years 1950 through 1990.
B)A linear model should be used for each pair of adjacent data points.
C)One linear model is appropriate for the years 1910 through 1970 and another linear model for the years 1970 through 1990.
D)A linear model should not be used for any part of the data.
E)A single linear model is appropriate for the entire data set.

Question

The scatterplot below shows the percentage of the US population that is foreign born for the years 1910 - 1990.For what range of years is a linear model appropriate? 
A)One linear model is appropriate for the years 1910 through 1950 and another linear model for the years 1950 through 1990. 
B)A linear model should be used for each pair of adjacent data points. 
C)One linear model is appropriate for the years 1910 through 1970 and another linear model for the years 1970 through 1990. 
D)A linear model should not be used for any part of the data. 
E)A single linear model is appropriate for the entire data set.

Quizplus · Accepted Answer

Looking at the scatterplot, it seems like there are two distinct groups of data points with a change in slope around the year 1970. Therefore, it makes sense to use two linear models, one for 1910-1970 and the other for 1970-1990. Choice A and B are incorrect as using two different linear models for each segment is not necessary. Choice D is also incorrect as a linear trend can be observed in the data. Choice E is not the best option as using a single linear model may not accurately capture the change in slope around 1970.

The Scatterplot Below Shows the Percentage of the US Population