Describing and Classifying Two-Variable Linear and Non Linear Relationships



when using scatter plots to model two variable data it's important to know how to describe the relationships that we are graphing one such method is to describe the independent variable increasing and what its effect will be on the dependent such as as the independent variable increases the dependent variable either increases or decreases so let's take a look at an example where the independent is age and the dependent is height now if we're talking about a child who's still growing we would assume that as the age increases the height of the child will also increase as we can see in the scatterplot describing the relationship might also involve whether the data is rising or falling to the right and in this case we can see that the data is rising to the right we would then look to see whether the data has a strong or weak relationship and in this case we can see it's pretty tight to the line of best fit so that would indicate a strong relationship we can then also speak in terms of positive or negative if rising to the right we suggest it's a positive trend if it's falling to the right it would be a negative trend so in this case we have a positive relationship and finally we want to know whether this is a linear relationship for example following a line of best fit or a non linear relationship such as following a curve so in this case it's pretty clear that we have a strong positive linear relationship let's look at another example where the independent variable is distance traveled and the dependent variable is fuel remaining in a gas tank so again describing this relationship might include suggesting that as distance traveled increases the fuel remaining will decrease as we can see in the scatterplot shown to the left we could also say that the data is falling to the right and again this relationship seems to be strong since the data is very tight to the line of best fit the data is falling to the right so that would be a negative trend and the data appears to follow a line rather than a curve so we would call that a linear relationship so we have a strong negative linear relationship in this example if we think back to the candle burning three-act math task that we referenced in the previous video we'll also notice that as time in minutes increases the height in centimeters will decrease as the candle burns down it appears that the data is falling to the right and we would classify this as a strong negative linear relationship

Michael Martin

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