Question

Two scatterplots are shown below. Scatterplot 1 A scatterplot has 14 points. The horizontal axis is labeled "x" and has values from 30 to 110. The ver

Scatterplots
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asked 2020-11-09
Two scatterplots are shown below.
Scatterplot 1
A scatterplot has 14 points.
The horizontal axis is labeled "x" and has values from 30 to 110.
The vertical axis is labeled "y" and has values from 30 to 110.
The points are plotted from approximately (55, 60) up and right to approximately (95, 85).
The points are somewhat scattered.
Scatterplot 2
A scatterplot has 10 points.
The horizontal axis is labeled "x" and has values from 30 to 110.
The vertical axis is labeled "y" and has values from 30 to 110.
The points are plotted from approximately (55, 55) steeply up and right to approximately (70, 90), and then steeply down and right to approximately (85, 60).
The points are somewhat scattered.
Explain why it makes sense to use the least-squares line to summarize the relationship between x and y for one of these data sets but not the other.
Scatterplot 1 seems to show a relationship between x and y, while Scatterplot 2 shows a relationship between the two variables. So it makes sense to use the least squares line to summarize the relationship between x and y for the data set in , but not for the data set in .

Answers (1)

2020-11-10
The least-squares line to summarize the relationship between x and y for the dataset that was used to construct the scatterplot 2 makes sense since the points are roughly scattered along the points (55, 55) steeply up and right to approximately (70, 90), and then steeply down and right to approximately (85, 60), an approximate relationship between x and y can established using linear square regression line because there exists a linear trend in the data.
The dataset used to construct the scatterplot 1 does not fit into a least-square line because the points are roughly scattered along the points (55, 60) in the y-axis and (95, 85) in the x-axis and there do not exists any linear trend among the points. Thus, if a least-square line is used to summarize the relationship between x and y it may not provide a best fit for the data.
Thus, it makes sense to use the least squares line to summarize the relationship between x and y for the data set in the scatterplot 2, but not for the data set in the scatterplot 1.
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