Lesson 12.5 Prediction

Prediction

Under certain conditions, you can use the line of best fit for estimating y when you know x. The conditions are:

• the scatter plot looks linear,
• the correlation coefficient r tells us that the relationship between x and y is significant, and
• x and y are related in a way that it is reasonable for y to be dependent upon x (for example, generally tall people weigh more than small people).

The process of estimating y when you know x is called prediction.

Example: A study is done to examine if women wearing larger size shoes tend to be taller. Let x = a woman's shoe size and y = her height, in inches.

The equation of the line of best fit is :

Let's predict a woman's height when her shoe size is 6 1/2. Let x = 6.5 and substitute the x value in the equation.

So, when a woman's show size is 6 1/2, her predicted height is about 61.8 inches.

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Caution

Do not use the regression equation to predict values outside the domain of x.

For the shoe size and height example above, x = 11 and x = 4 are outside the domain of x, so do not try to use the regression equation to predict the heights.

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Think About It

For the woman's shoe size and height example, predict the heights given the following shoe sizes. The equation is:

• shoe size = 9 1/2.
• shoe size = 8 1/2. Why is the predicted y different from the actual y?
• shoe size = 11 1/2. (Caution!)

NOTE: We use technology (TI-83 or TI-84 calculators) to perform the calculations for linear regression and then we use the regression equation to make predictions.

Please continue to the next section of this lesson.

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Up » 12.1 Linear Equations » 12.2 Scatter Plots » 12.3 The Regression Equation » 12.4 The Correlation Coefficient » 12.5 Prediction » 12.6 Outliers » 12.7 TI-83