Question

A linear regression equation for a data set has a correlation coefficient of r=0.4. Would you be confident using your equation to predict what will happen outside of the data set?

Answer 1

1. If by "outside of the data set" you mean "out of your data's range", the answer is no.
2. To know if your model fits your data, use the `"R"^2`

Explanation:

1. You cannot use a model for prediction out of the range of the dataset.

Why ? Because you simply have no idea of the shape of the relationship out of your data's range.

For example, let's see the graph below. Let's say that your data are the black dots. The dotted lines represent your data's range. A linear relationship would well fit to your data and you can apply your model inside the range.
However, outside the range, the data do not follow a linear relationship anymore. So, you cannot predict them with the relation you applied to your data.

1. Let's say you want to predict values in the range of your dataset.

To know if your model fits your data correctly, you should look at the `"R^2"`.
In fact, the correlation coefficient measure the strength of the relation between X and Y, and will not say anything about your model.
The `"R^2"` will tell you the amount of variance explained by your model (how close to your data your model is ). The good value for `"R^2"` depends of the field of study you are working in.