12.5 Prediction
Substituting x-values into the best-fit line to estimate y, and why estimates outside the range of the observed data cannot be relied on.
14 exercises
12.5 Exercise 1
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?
b. What would you predict the final exam score to be for a student who scored a 90 on the third exam?
12.5 Exercise 3
ŷ = 101.32 + 2.48x where ŷ is in thousands of dollars.
What would you predict the sales to be on day 60?
12.5 Exercise 5
ŷ = 1350 – 1.2x where x is the number of hours and ŷ represents the number of acres left to mow.
How many acres will be left to mow after 20 hours of work?
12.5 Exercise 7
ŷ = 1350 – 1.2x where x is the number of hours and ŷ represents the number of acres left to mow.
How many hours will it take to mow all of the lawns? (When is ŷ = 0?)
12.5 Exercise 9
Perform linear regression. What is the linear equation? Round to the nearest whole number.
12.5 Exercise 11
Solve.
- When x = 1985, ŷ = _____
- When x = 1990, ŷ =_____
- When x = 1970, ŷ =______ Why doesn’t this answer make sense?
12.5 Exercise 13
What does the correlation imply about the relationship between time (years) and the number of diagnosed flu cases reported in the U.S.?
12.5 Exercise 15
Write the equation: ŷ= ____________
12.5 Exercise 17
Does the line seem to fit the data? Why or why not?
12.5 Exercise 19
What does the correlation imply about the relationship between time (years) and the number of diagnosed flu cases reported in the U.S.?
12.5 Exercise 21
Enter your data into your calculator or computer. The pre-1981 data should not be included. Why is that so?
Write the linear equation, rounding to four decimal places:
12.5 Exercise 23
Recently, the annual number of driver deaths per 100,000 for the selected age groups was as follows:
- For each age group, pick the midpoint of the interval for the x value. (For the 75+ group, use 80.)
- Using “ages” as the independent variable and “Number of driver deaths per 100,000” as the dependent variable, make a scatter plot of the data.
- Calculate the least squares (best–fit) line. Put the eq…
12.5 Exercise 25
The maximum discount value of the Entertainment® card for the “Fine Dining” section, Edition ten, for various pages is given in the table
- Decide which variable should be the independent variable and which should be the dependent variable.
- Draw a scatter plot of the ordered pairs.
- Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
- Find the correlation coefficient. Is it…
12.5 Exercise 27
We are interested in whether or not the number of letters in a state name depends upon the year the state entered the Union.
- Decide which variable should be the independent variable and which should be the dependent variable.
- Draw a scatter plot of the data.
- Does it appear from inspection that there is a relationship between the variables? Why or why not?
- Calculate the least-squares line. Put th…
Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.