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.
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 + 2.8x.