Suppose that a linear model is appropriate when comparing the height of children to age. The heights of 30 children, aged 5 to 9, are recorded. When do we expect this linear model to give reasonable approximations?

The linear model will give a good approximation if the new value is within or close to the values we used to construct the linear model.

Step-by-step explanation:

A linear model gives reasonable approximations under these two conditions:

If the value for which we need to use the approximation is within the range of values we used to construct the linear model If the value for which we need to use the approximation is close to the values which we used to construct the linear model.

For the given model, heights of children aged 5 to 9 were recorded. Here, age is the independent variable and height will be the independent variable. Heights of 30 children from age 5 to 9 were recorded and a linear model was constructed. Now, we need to tell which value of age can be made an input of this function to find the approximate height.

Using the above two principles, the linear model will give a good approximate if:

The age of the child is between 5 and 9 years. In this situation, the value approximated by the model will be closer to the actual height in majority of the cases. For example, the model will give good approximations for children of ages 6, 6.5, 7, 7.75 etc The age of child is close to 5 and 9 years old but outside the range. In this case, the model will also give good approximations. For example. for a child of age 4.5 years or 10 years, the model will still give a good and reasonable approximations.