Statistics

# 12.4Prediction (Optional)

Statistics12.4 Prediction (Optional)

Recall the third exam/final exam example.

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 mean final exam score of statistics students who received a 73 on the third exam. The exam scores (x values) range from 65 to 75. Since 73 is between the x values 65 and 75, substitute x = 73 into the equation. Then,

$y^ =−173.51+4.83(73)=179.08 . y^ =−173.51+4.83(73)=179.08 .$

We predict that statistics 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 12.10

Recall the third exam/final exam example.

### Problem

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

### Problem

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

## Try It 12.10

Data are collected on the relationship between the number of hours per week practicing a musical instrument and scores on a math test. The line of best fit is as follows:

ŷ = 72.5 + 2.8x.
What would you predict the score on a math test will be for a student who practices a musical instrument for five hours a week?

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