12.4 Prediction (Optional)

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?

Recall the third exam/final exam example.

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

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?

Use the following information to answer the next two exercises. An electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where x is the day. The model can be written as ŷ = 101.32 + 2.48x, where ŷ is in thousands of dollars.

What would you predict the sales to be on day 60?

Use the following information to answer the next three exercises. A landscaping company is hired to mow the grass for several large properties. The total area of the properties is 1,345 acres. The rate at which one person can mow is ŷ = 1350 – 1.2x, where x is the number of hours and ŷ represents the number of acres left to mow.

How many acres are left to mow after 20 hours of work?

Use the following information to answer the next three exercises. A landscaping company is hired to mow the grass for several large properties. The total area of the properties is 1,345 acres. The rate at which one person can mow is ŷ = 1350 – 1.2x, where x is the number of hours and ŷ represents the number of acres left to mow.

How many hours does it take to mow all the lawns, or when is ŷ = 0?…

Perform a linear regression. What is the linear equation? Round to the nearest whole number. Find the following:

Write the equations:

1. Linear equation: __________
2. a = ________
3. b = ________
4. r = ________
5. n = ________

Solve.

1. When x = 1985, ŷ = _____.
2. When x = 1990, ŷ = _____.
3. When x = 1970, ŷ = _____. Why doesn’t this answer make sense?

What does the correlation imply about the relationship between time (years) and the number of diagnosed flu cases reported in the United States?

Plot the two points on the graph. Then, connect the two points to form the regression line.

Write the equation: ŷ = ____________.

Does the line seem to fit the data? Why or why not?

What does the correlation imply about the relationship between time (years) and the number of diagnosed flu cases reported in the United States?

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.

Calculate the following:

1. a = _____
2. b = _____
3. correlation = _____
4. n = _____

Recently, the annual numbers of driver deaths per 100,000 people for the selected age groups are as follows:

1. For each age group, pick the midpoint of the interval for the x value. For the 75+ group, use 80.
2. Using age as the independent variable and number of driver deaths per 100,000 people as the dependent variable, make a scatter plot of the data.
3. Calculate the least-squares (best–fit) line. Put…

The maximum discount value of the Entertainment^® card for the Fine Dining section, 10th edition, for various pages is given in the table.

1. Decide which variable should be the independent variable and which should be the dependent variable.
2. Draw a scatter plot of the ordered pairs.
3. Calculate the least-squares line. Put the equation in the form ŷ = a + bx.
4. Find the correlation coefficient. Is it sign…

We are interested in whether the number of letters in a state name depends on the year the state entered the Union.

1. Decide which variable should be the independent variable and which should be the dependent variable.
2. Draw a scatter plot of the data.
3. Does it appear from inspection that there is a relationship between the variables? Why or why not?
4. Calculate the least-squares line. Put the equation…