# Predicting Y from X

One of the important concepts to understand about a scatterplot with a regression line is just how the regression line helps us to predict Y. The applet entitled PredictY, shown below, illustrates this simple principle. As you move the slider on the X axis you vary the value of X, and can read the corresponding value of Y. In this example, for X = 2, Y = 2.2. Additionally, by moving the sliders on the left and right, you can vary the intercept and the slope, respectively, and observe how the predictions change.

 Bottom slider moves the value of X along the horizontal axis. Observe how the linked Y value changes as X changes. Left and right scrollbars change the intercept and slope, respectively, of the line.
• Calculate values for X = 2, 3, and 4.
• Make the slope steeper, by moving the slider on the right up, and again calculate for X = 2, 3, and 4. What has changed?
• Now do the same thing, except this time change the intercept. Now how do the values of change as we vary X?