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Can you think of a situation in which a trend line does not provide an accurate prediction?
No
We often use linear models to make predictions about y-values for a set of data presented in a scatter plot. We want to decide if we can always use the model in the opposite direction, to predict the x-value when we know the y-value. Let's consider an example.
In the example, on the x-axis we have the number of children in a family and on the y-axis we have the number of boxes of cereal consumed by the family per month. Let's add a trend line to our graph.
Now let's assume that we want to predict the x-value when y= 5. To do so, we can use our trend line and find the value of x that corresponds to y= 5.
Our prediction suggests that a family with 4.5 children consumes 5 boxes of cereals. This result does not make sense because we cannot have a half of a child. We can think of other examples. Let's again try to predict the x-values using our trend line.
| Possible Situation | Boxes of Cereal per Month | Real Number of Children | Predicted Number of Children | Is Prediction Accurate? |
|---|---|---|---|---|
| A family with no children loves cereal and they usually consume about 5.5 boxes per month. | 5.5 | 0 | 5 | No * |
| A family with 4 children does not like cereal very much and they consume only 1 box per month. | 1 | 4 | 0 | No * |
Additionally, many families with different numbers of children can consume the same amount of cereal. The linear model could not provide an accurate prediction in these situations as well. Based on these examples we can see that, a linear model can not always be used to make a prediction about any x-value.
