12.5 Outliers

Using this new line of best fit (based on the remaining 10 data points in the third exam/final exam example), what would a student who receives a 73 on the third exam expect to receive on the final exam? Is this the same as the prediction made using the original line?

The data points for the graph from the third exam/final exam example are as follows: (1, 5), (2, 7), (2, 6), (3, 9), (4, 12), (4, 13), (5, 18), (6, 19), (7, 12), and (7, 21). Remove the outlier and recalculate the line of best fit. Find the value of ŷ when x = 10.

Marcus states that all outliers are influential points. Is he correct? Explain.

Do there appear to be any outliers?

What effect did the potential outlier have on the line of best fit?

The sum of squared errors (SSE) for a data set of 18 numbers is 49. What is the standard deviation?

Given the information in Table 12.30, which represents the relationship between final exam math grades and final exam history grades, decide whether point (56, 95) is an influential point. Explain how you arrived at your decision. Show all work.

Ornithologists (scientists who study birds) tag sparrow hawks in 13 different colonies to study their population. They gather data for the percentage of new sparrow hawks in each colony and the percentage of those that have returned from migration.

Percent return: 74, 66, 81, 52, 73, 62, 52, 45, 62, 46, 60, 46, 38
Percent new: 5, 6, 8, 11, 12, 15, 16, 17, 18, 18, 19, 20, 20

1. Enter the data into a ca…

The following table consists of one student athlete’s time (in minutes) to swim 2,000 yards and the student’s heart rate (beats per minute) after swimming on a random sample of 10 days.

1. Enter the data into a calculator and make a scatter plot.
2. Use the calculator’s regression function to find the equation of the least-squares regression line. Add this to your scatter plot from Part A.
3. Explain what…

Use the data in the Table 12.35 to determine the linear regression line equation with the outliers removed. Is there a linear correlation for the data set with outliers removed? Justify your answer.

The average number of people in a family who attended college for various years is given in the table.

1. Using year as the independent variable and number of family members attending college as the dependent variable, draw a scatter plot of the data.
2. Calculate the least-squares line. Put the equation in the form ŷ = a + bx.
3. Does the y-intercept, a, have any meaning here?
4. Find the correlation coeffic…

The percent of female wage and salary workers who are paid hourly rates is given in the table for the years 1979 to 1992.

1. Using year as the independent variable and percent of workers paid hourly rates as the dependent variable, draw a scatter plot of the data.
2. Does it appear from inspection that there is a relationship between the variables? Why or why not?
3. Does the y-intercept, a, have any mean…

1. Complete the table for the cost per ounce of the different sizes of laundry detergent.
2. Using size as the independent variable and cost per ounce as the dependent variable, 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 in the form ŷ = a + bx.
5. Find the correlation…

The following are advertised sale prices of color televisions at Anderson’s:

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 in the form ŷ = a + bx.
5. Find the correl…

We are interested in whether there is a relationship between the ranking of a state and the area of the state.

1. What are the independent and dependent variables?
2. What do you think the scatter plot will look like? Make 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 in th…