It can be somewhat subjective to compare the strength of one association to another. This is true whether the pattern is linear, nonlinear, positive, or negative. The strength of the relationship or association between two variables is shown by how close the points are to each other. This is seen as a linear pattern that falls from left to right. In a negative pattern, as the predictor increases, the value of the response decreases. This shows up in the scatterplot as a linear pattern that rises from left to right. In a positive pattern, as the value of the predictor increases, so does the value of the response. If there is no clear pattern, then it means there is no clear association or relationship between the variables that we are studying.Īs you can see above, linear patterns can be thought of as either positive or negative. Whatever the pattern is, we use this to describe the association between the variables. Scatterplots with a linear pattern have points that seem to generally fall along a line while nonlinear patterns seem to follow along some curve. In general, you can categorize the pattern in a scatterplot as either linear or nonlinear. Each point represents the value of the response for a given value of the predictor. Using this terminology, a scatterplot is used to understand how the response responds to changes in the predictor. Given a scatterplot, the variable on the horizontal axis is the predictor (or independent variable) and the variable on the vertical axis is the response (or dependent variable). Questions like “When the temperature increases, do gas prices also increase?” or “How are changes in the price of gas related to the number of miles people drive each month?” can be answered by studying the pattern in a scatterplot. Since 10mm is much higher than the highest rainfall recorded, we cannot assume that the line of best fit would still follow the pattern when the rainfall is 10mm, so the value of 64 umbrellas is not a reliable estimate.Scatterplots are used to understand the relationship or association between two variables. This process is called extrapolation, because the value we are using is outside the range of data used to draw the scatter graph. This gives a value of approximately 64 umbrellas sold. If there was 10mm of rainfall, we could extend the graph and the line of best fit to read off the number of umbrellas sold. Draw a line by going across from 3 mm and then down.Īn estimated 19 umbrellas would be sold if there was 3 mm of rainfall. The value of 3mm is within the range of data values that were used to draw the scatter graph.įind where 3 mm of rainfall is on the graph. To estimate the number sold for 3mm of rainfall, we use a process called interpolation. For example, how many umbrellas would be sold if there was 3mm of rainfall? What if there was 10mm of rainfall? The line of best fit for the scatter graph would look like this: Interpolation and extrapolationįrom the diagram above, we can estimate how many umbrellas would be sold for different amounts of rainfall. It should also follow the same steepness of the crosses. Lines of best fitĪ line of best fit is a sensible straight line that goes as centrally as possible through the coordinates plotted. No correlation means there is no connection between the two variables. Negative correlation means as one variable increases, the other variable decreases. Positive correlation means as one variable increases, so does the other variable. Graphs can either have positive correlation, negative correlation or no correlation. If data plotted on a scatter graph shows correlation, we cannot assume that the increase in one of the sets of data caused the increase or decrease in the other set of data – it might be coincidence or there may be some other cause that the two sets of data are related to. However, it is important to remember that correlation does not imply causation. On days with higher rainfall, there were a larger number of umbrellas sold. The graph shows that there is a positive correlation between the number of umbrellas sold and the amount of rainfall. The number of umbrellas sold and the amount of rainfall on 9 days is shown on the scatter graph and in the table. Scatter graphs are a good way of displaying two sets of data to see if there is a correlation, or connection.
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