RELATIONSHIPS IN DATA
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The line on this graph is the trend line; it is the line that best describes the data. About half of the points should be on either side of the line. You may notice that outliers are practically ignored when a trend line is drawn. This trend line goes from the lower left to the upper right and shows a positive relationship.
You can also see that the trend line also goes off of the chart as it is an arrow and thus continues in the same direction. Therefore, you could use a chart like this one to predict the trend. It is likely that the trend will continue to go up. |
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Take a look at this scatterplot to the left.
There is a trend between the independent and dependent values of the chart. If you were to draw a line of best fit, you would see that the relationship between these variables is moving up to the right. Trends that move up and to the right show a positive correlation.
There are three trends, positive, negative, and no relationship. Here is what they look like:
There is a trend between the independent and dependent values of the chart. If you were to draw a line of best fit, you would see that the relationship between these variables is moving up to the right. Trends that move up and to the right show a positive correlation.
There are three trends, positive, negative, and no relationship. Here is what they look like:
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POSITIVE RELATIONSHIP
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NEGATIVE RELATIONSHIP
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NO RELATIONSHIP
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This is a positive relationship. As the x-values increase, the y-values increase. Some points may not follow an exact pattern but the overall trend, the general tendency or movement, is clearly from the lower left to the upper right of the plot.
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This is a negative relationship. In this case, as the x-values increase, the y-values decrease. You may argue that the slope is not as steep which is true. However, the general tendency is evident. This graph moves from the upper left to the lower right.
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At times, like the one shown above, there is no relationship between variables. The scatterplots of these situations will show no trend. In other words, there seems to be no definite pattern with the points; you cannot see any particular direction that they take.
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Let’s think about some real life scenarios:
What happens to people’s heating bills as the temperature outside increases?
Put the temperature outside on the x-axis and the cost of the heating bills on the y-axis.
What happens to the gasoline consumption in a vehicle as more miles are travelled?
Put miles travelled on the x-axis and gasoline consumption on the y-axis.
What happens to the number of accidents as the number of blue cars increases on the road?
Put the number of blue cars on the x-axis and the number of accidents on the y-axis.
What happens to people’s heating bills as the temperature outside increases?
Put the temperature outside on the x-axis and the cost of the heating bills on the y-axis.
- As the temperature outside decreases, people's heating bills go down as they use less energy to heat their home.
- As one variable goes up, the other goes down.
What happens to the gasoline consumption in a vehicle as more miles are travelled?
Put miles travelled on the x-axis and gasoline consumption on the y-axis.
- As the miles traveled in a car go up, the amount of gasoline consumed also goes up.
- As one variable goes up, the other goes up, too.
What happens to the number of accidents as the number of blue cars increases on the road?
Put the number of blue cars on the x-axis and the number of accidents on the y-axis.
- As the number of blue cars increases the number of accidents may go up, down, or stay the same.
- The number of accidents is independent of the number of blue cars.
This text was adapted from CK12.com. It is licensed under the Creative Commons (CC BY-NC 3.0)