We are interested in whether there is a relationship between the rank of a state and the year it entered the Union.
Let year be the independent variable and rank be the dependent variable.
What do you think the scatter plot will look like? Make a scatter plot of the data.
Why must the relationship be positive between the variables?
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. What does it imply about the significance of the relationship?
Let’s say a fifty-first state entered the union. Based upon the least squares line, when should that have occurred?
Using the least squares line, how many states do we currently have?
Why isn’t the least squares line a good estimator for this year?
0.9553
1934
Below are the percents of the U.S. labor force (excluding self-employed and unemployed ) that are members of a union. We are interested in whether the decrease is significant. (Source:
Bureau of Labor Statistics, U.S. Dept. of Labor )
Year
Percent
1945
35.5
1950
31.5
1960
31.4
1970
27.3
1980
21.9
1993
15.8
2011
11.8
Let year be the independent variable and percent be the dependent variable.
What do you think the scatter plot will look like? Make a scatter plot of the data.
Why will the relationship between the variables be negative?
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. What does it imply about the significance of the relationship?
Based on your answer to (e), do you think that the relationship can be said to be decreasing?
If the trend continues, when will there no longer be any union members? Do you think that will happen?
The next two questions refer to the following information: The data below reflects the 1991-92 Reunion Class Giving. (Source:
SUNY Albany alumni magazine )
Class Year
Average Gift
Total Giving
1922
41.67
125
1927
60.75
1,215
1932
83.82
3,772
1937
87.84
5,710
1947
88.27
6,003
1952
76.14
5,254
1957
52.29
4,393
1962
57.80
4,451
1972
42.68
18,093
1976
49.39
22,473
1981
46.87
20,997
1986
37.03
12,590
We will use the columns “class year” and “total giving” for all questions, unless otherwise stated.
What do you think the scatter plot will look like? Make a scatter plot of the data.
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. What does it imply about the significance of the relationship?
For the class of 1930, predict the total class gift.
For the class of 1964, predict the total class gift.
For the class of 1850, predict the total class gift. Why doesn’t this value make any sense?
0.8302
$1577.46
$11,642.66
-$22,105.34
We will use the columns “class year” and “average gift” for all questions, unless otherwise stated.
What do you think the scatter plot will look like? Make a scatter plot of the data.
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. What does it imply about the significance of the relationship?
For the class of 1930, predict the average class gift.
For the class of 1964, predict the average class gift.
For the class of 2010, predict the average class gift. Why doesn’t this value make any sense?
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Source:
OpenStax, Collaborative statistics (custom online version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11476/1.5
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