Question

what is the difference between strength and fit when interpreting regression equations? do we always need to report and discuss both?

Answer 1

There is a difference between strength & fit when interpreting regression equations.

Strength gives an idea about how the variables are strongly related or correlated. Before fitting a regression model, we need to check whether the relationship between dependent & independent variable exists. This can be done through the scatter plot of variables. If you see the summary of output of a regression model, you will get value R^2 which is nothing but a square of the correlation coefficient. This gives an idea about the proportion of variation independent variable explained by the independent variable.

Fit gives us an idea about the change independent variable by the change in an independent variable. For eg: Let Y=3 +5*X. Here, the coefficient of X implies that if we change the value of x by 1 unit then y will change by 5. After fitting a model on the given data, we can also predict the value of Y for the new value of X.

We always need to report and discuss both because the output of any regression model gives both things. You have to interpret in the report.