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Prediction

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: Linear Regression and Correlation: Prediction is a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean with contributions from Roberta Bloom.

Recall the third exam/final exam example.

We examined the scatterplot and showed that the correlation coefficient is significant. We found the equation of the best fit line for the final exam grade as a function of the grade on the third exam. We can now use the least squares regression line for prediction.

Suppose you want to estimate, or predict, the final exam score of statistics students who received 73 on the third exam. The exam scores (xx-values) range from 65 to 75. Since 73 is between the xx-values 65 and 75, substitute x=73x=73 into the equation. Then:

y ^ = -173.51 + 4.83 ( 73 ) = 179.08 y ^ =-173.51+4.83(73)=179.08
(1)

We predict that statistic students who earn a grade of 73 on the third exam will earn a grade of 179.08 on the final exam, on average.

Example 1

Recall the third exam/final exam example.

Problem 1

What would you predict the final exam score to be for a student who scored a 66 on the third exam?

Solution

145.27

Problem 2

What would you predict the final exam score to be for a student who scored a 90 on the third exam?

Solution

The x values in the data are between 65 and 75. 90 is outside of the domain of the observed x values in the data (independent variable), so you cannot reliably predict the final exam score for this student. (Even though it is possible to enter x into the equation and calculate a y value, you should not do so!)

To really understand how unreliable the prediction can be outside of the observed x values in the data, make the substitution x = 90 into the equation.

y ^ = -173.51 + 4.83 ( 90 ) = 261.19 y ^ =-173.51+4.83(90)=261.19

The final exam score is predicted to be 261.19. The largest the final exam score can be is 200.

Note:
The process of predicting inside of the observed x values in the data is called interpolation. The process of predicting outside of the observed x values in the data is called extrapolation.

**With contributions from Roberta Bloom

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks