Scatter Plots : Introduction to Positive and Negative Correlation

By | 04/05/2025
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Scatter Plots : Introduction to Positive and Negative Correlation/a>

so this lesson looks at Scatter Plots and what we’re going to do is look at uh different types of correlations that you might observe in a scatter plot now Scatter Plots are just a collection of ordered pairs of and um on a graph and in some cases the graph looks like just a bunch of dots all over the place in others there’s a general uh Trend or a general shape to the graph and so if we take a look at this example the there doesn’t seem to a straight line relationship between the X and the Y variables however the overall is a general upward Trend and so what we say is that as one um variable increase increases so for example as X increases y increases as well so this is what we call positive correlation and so when X increases if the value of the other value of y increases as well then we say that’s posit POS of correlation and so that when one variable value goes up the other goes up as well and an example of positive correlation is if you were to look at the um height of a child over time then as a child gets over go as the child gets older then the height of the child increases and so if we take a look at data here as age increases then the height of the child increases as well and so that this would be an example of positive correlation and the growth might not necessarily be L linear some linear May grow faster than others but overall as time passes the child gets taller so as um height as age increases height increases so that’s an example of positive correlation an example of NE negative correlation would be where as one variable increases in this case as X increases the value of y decreases and so this would be negative um this has a negative uh relationship as far as um the two variables in fact as one goes up the other goes down and so as we said this is an example of negative correlation in other words as one variable increases the other decreases and we can see that graphically as as one goes up the other goes down so example of negative correlation is if if you buy a car the older gets the value of it decreases and so this would be an example of negative correlation early on if the car as a car is new it’s worth more as it gets older as the age of the car increases the value of the car decreases so this would be an example of negative correlation and example of no correlation is where there seems to be no pattern at all as X increases here well sometimes uh why decreases sometimes it increases so there seems to be no connection or no relationship between these two variables and if you take a look at baseball players and their bodying average you’ll find that there’s some uh some people with uh small shoes are good batters and some people with big shoes are good batters and vice versa some of them are not good batters so overall there’s no relationship between the ability to hit a baseball and your shoe size so that’s no correlation and so if we’re taking a look at a series of uh Scatter Plots here and which we asked which ones are linear which ones show a correlation well here this would be no correlation and here there doesn’t seem to be any kind of trend maybe a little bit of a downward Trend here but it’s hard to really tell with this one this one however does have um seem to have a linear Trend and D well this one doesn’t seem to have any correlation at all e however does have a linear Trend and the line seems to go the pattern seems to be as one increases the other increases as well and this one has a linear Trend as well so this since um as the dependent independent variable increases the dependent variable decreases here so this would be an example of negative correlation and this one as one Inc variable increases the other increases as well so this would be positive correlation and since there is really um as one increases the other variable stays constant this is called constant correlation and if we’re going to take a look at um skip um Scatter Plots and interpret them if we take a look at sport utility vehicles in the US and over time over a number of years and the sales in millions of dollars and you’ll note that as time goes by there is an increase over the number of um SUVs that were sold in the US so if we’re going to graph this on a grid What you’re going to find is that there is actually a positive correlation here because when we plot these points and just plotting the points here so here’s 1994 and 1.6 1995 and 1.7 Etc so we plot these points and note that they’re not in a straight line relationship but the Trend appears linear here and because it’s generally a pattern of uh going up the trend is increasing as years increase SUV sales increase so this is an example of positive correlation again and if we’re going to predict the sales in 2001 well then it would be right about here which we 3 and a half million um SUV sales that was before the gas pric has jumped so if we were to plot the SP amount of time spent watching TV and the time spent on homework then what we and put this onto a grid then what we would find as we plot these points on the grid and so the data is coming from over here the trend appears linear however as um number of hours spent watching TV increases the time spent on homework seems to decrease and so that means that there is negative correlation here

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