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# Scatterplots and correlation review

A scatterplot is a type of data display that shows the relationship between two numerical variables. Each member of the dataset gets plotted as a point whose x-y coordinates relates to its values for the two variables.

## What is a scatterplot?

A scatterplot is a type of data display that shows the relationship between two numerical variables. Each member of the dataset gets plotted as a point whose $\left(x,y\right)$ coordinates relates to its values for the two variables.
For example, here is a scatterplot that shows the shoe sizes and quiz scores for students in a class:
Each data point is a student whose $x$-coordinate gives their shoe size and $y$-coordinate gives their quiz score.
Want to learn more about constructing scatterplots? Check out this video.

## What is correlation?

We often see patterns or relationships in scatterplots.
When the $y$ variable tends to increase as the $x$ variable increases, we say there is a positive correlation between the variables.
$\text{Positive correlation}$
When the $y$ variable tends to decrease as the $x$ variable increases, we say there is a negative correlation between the variables.
$\text{Negative correlation}$
When there is no clear relationship between the two variables, we say there is no correlation between the two variables.
$\text{No correlation}$
Want to learn more about types of correlation? Check out this video.

## Practice

problem 1
The graph shown below shows the relationship between the age of drivers and the number of car accidents per $100$ drivers in the year $2009$.
What is the best description of this relationship?

Want to practice more problems like these? Check out this exercise on positive and negative correlations.

## Want to join the conversation?

• Would a V shaped scatter plot have positive correlation, negative correlation, or no correlation?
• If a V shaped scatter plot is perfectly symmetric, there would be no (linear) correlation. So if a V shaped scatter plot is nearly symmetric, there is expected to be little or no (linear) correlation.
• If you had an "O" shape, would it have a positive, negative, or no linear relationship?
• If it was a perfectly symmetrical shape, there would be no correlation, but in real life that wouldn't happen. So if there was a scatterplot where all of the points formed a near 'O' shape, there would be very little correlation.
(1 vote)
• I feel good about my knowledge of scatter plots.
• if you had an X shape as the scatter plot would that have a negative, positive or no correlation
• It is unlikely that there wouldn't be any correlation at all, but it would be very weak for sure, so the correlation coefficient would tend towards zero, and thereby the slope of the regression line would also be close to zero.
• what correlation would a straight vertical line scatter plot be
• A straight vertical line scatter plot would indicate a perfect negative or positive correlation, depending on the direction of the line. If all the points fall exactly on a straight vertical line from top to bottom, it suggests a perfect negative correlation, meaning that as one variable increases, the other decreases linearly. Similarly, if all the points fall on a straight vertical line from bottom to top, it suggests a perfect positive correlation, indicating that as one variable increases, the other increases linearly.
(1 vote)
• What makes it non linear?
• Not linear is when there has no tendency to be 'up a ravine or down a ravine'
(1 vote)
• What if the data is clumping in one corner?
• Then it would have no linear correlation, and should be marked as having no correlation/no linear correlation.
• why does the no association plots always have to be in a cluster to be identified as no association plots?
(1 vote)
• The term "no association" in the context of scatterplots refers to the absence of a clear pattern or relationship between the two variables being plotted. While scatterplots with no association may sometimes exhibit clustering of data points, especially if there's random variation or noise present in the data, this is not a requirement. Scatterplots with no association can have data points scattered across the plot with no discernible pattern or trend. However, it's essential to examine the overall distribution of points to determine whether there's any systematic relationship between the variables or if they're randomly distributed. If there's no apparent relationship, it's classified as having no association.
(1 vote)
• Mary is making a scatter plot from two data sets. One set of data gives the amount of precipitation in inches. The second data set is the number of umbrellas sold. Which type of correlation would you expect?