# Introduction

### Introduction

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,

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 12.11

Recall the third exam/final exam example.

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

a. 145.27

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

b. The *x* values in the data are between 65 and 75. Ninety is outside 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 90 into the equation for *x* and calculate a corresponding *y* value, the *y* value that you get will not be reliable.

*x*values observed in the data, make the substitution

*x*= 90 into the equation

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

*ŷ* = 72.5 + 2.8*x.*