Using Regression Lines for Prediction

Linear regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of another variable.

More precisely, if X and Y are two related variables, then linear regression analysis helps us to predict the value of Y for a given value of X or vice verse.

Using regression to make predictions doesn’t necessarily involve predicting the future. Instead, you predict the mean of the dependent variable given specific values of the independent variable(s). For our example, we’ll use one independent variable to predict the dependent variable. We measured both of these variables at the same point in time.

Photograph of a crystal ball that a psychic uses to make predictions. Psychic predictions are things that just pop into mind and are not often verified against reality. Unsurprisingly, predictions in the regression context are more rigorous. We need to collect data for relevant variables, formulate a model, and evaluate how well the model fits the data.

But suppose the correlation is high; do you still need to look at the scatterplot? Yes. In some situations the data have a somewhat curved shape, yet the correlation is still strong; in these cases making predictions using a straight line is still invalid. Predictions in these cases need to be made based on other methods that use a curve instead.

• Regression explores significant relationships between dependent variable and independent variable
• Indicates the strength of impact of multiple independent variables on a dependent variable
• Allows us to compare the effect of variable measures on different scales and can consider nominal, interval, or categorical variables for analysis.

Linear regression does not test whether data is linear. It finds the slope and the intercept assuming that the relationship between the independent and dependent variable can be best explained by a straight line.

One can construct the scatter plot to confirm this assumption. If the scatter plot reveals non linear relationship, often a suitable transformation can be used to attain linearity.