# Sketch a scatterplot where the association is nonlinear, but the correlation is close to [r = -1].

Question
Scatterplots
Sketch a scatterplot where the association is nonlinear, but the correlation is close to [r = -1].

2020-10-27
An association is nonlinear when there is some curvature present in the scatterplot.
The correlation is close to [r = —1], when the pattern slopes downwards strongly and the points do not deviate much from this sloping downwards pattern.
For example, the following graph then has a correlation close to [r = —1] while also being nonlinear (note: The correlation of this particular graph is 0.8941).

### Relevant Questions

Sketch a scatterplot where the association is linear, but the correlation is close to [r = 0].
The value of s alone doesn't reveal information about the form of an association. Sketch a scatterplot showing a nonlinear association with a small value of s and a second scatterplot showing a linear association with a large value of s.
Sketch a scatterplot showing data for which the correlation is [r = -1].
Make a scatterplot for each set of data. Tell whether the data show a linear association or a nonlinear association.
(1,2),(7,9.5),(4,7),(2,4.2),(6,8.25),(3,5.8),(5,8),(8,10),(0,0)
In this exercise, you will use the correlation and regression applet to create scatter plots with 10 points that have a correlation close to 0.7. The lesson here is that many models may have the same correlation. Always compile your data before trusting correlations. (a) Stop after adding the first two points. What is the value of correlation?
r=?
Why does correlation matter? Two is the minimum number of data points required to calculate the correlation. This value is the default correlation.
Because two points define a line, correlation always matters.
The mean of these two values always has this value.
Use a scatterplot and the linear correlation coefficient r to determinewhether there is a correlation between the two variables.
[x 1 2 2 5 6 y 2 5 4 15 15]
A researcher investigating the association between two variables collected some data and was surprised when he calculated the correlation.
He had expected to find a fairly strong association, yet the correlation was near 0.
Discouraged, he didn't bother making a scatterplot.
Explain to him how the scatterplot could still reveal the strong association he anticipated.
Sketch a scatterplot in which the presence of an outlier decreases the observed correlation between the response and explanatory variables. Indicate on your plot which point is the outlier.
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 .
The accompanying data on y = normalized energy $$\displaystyle{\left[{\left(\frac{{J}}{{m}^{{2}}}\right)}\right]}$$ and x = intraocular pressure (mmHg) appeared in a scatterplot in the article “Evaluating the Risk of Eye Injuries: Intraocular Pressure During High Speed Projectile Impacts” (Current Eye Research, 2012: 43–49), an estimated regression function was superimposed on the plot.