chapter 6 Measures of association & correlation in business
James is analyzing data for his final class. His teacher asked him to conduct a Pearson R test and to interpret the result. When calculating the Pearson R, James determined the increase of one variable correlates with a strong decrease of the other variable. What is the MOST likely value of the Pearson R Coefficient? -0.21 0.91 0 -0.87
-0.87
What is the range of the coefficient value?
-1.00 to 1.00
Which of the following Pearson Coefficients is MOST statistically significant? A coefficient with a p-value of 0.01 A coefficient with a p-value of 0.5 A coefficient with a p-value of 0.92 A coefficient with a p-value of 0.05
0.01
You are a research assistant for an important study. The lead psychologist on the study hands you the following data and asks you to find the Pearson coefficient. Which of the following numbers would you use for your 'n' value?
6
To plot a scatterplot, the researcher must have: Two variables. A reason to suspect they are connected. Numerical data. All of the above
All of the above
A scientist plots data points from an experiment, and notices that the dependent variables and the independent variables in the data set are decreasing together. What kind of correlation have they discovered, and why?
A positive correlation, because these describe situations where the dependent variables and the independent variables in a data set increase or decrease together.
What does r represent?
correlation coefficient.
Which of the following best describes a scatterplot?
A visual representation of the relationship between two variables.
A scientist finishes an experiment, and concludes that there is a causal link between the independent variable and the dependent variable. Why might they come to this conclusion?
Because changes in the independent variable appear to cause changes in the dependent variable.
A scientist is designing an experiment with rats, and designates weight as the dependent variable. Why might this be the case?
Because the weight will be influenced by an outside factor that the scientist controls.
How is the standard correlation coefficient derived?
By using the differences between those individual values and their averages
How can you access the CORREL function in Excel?
Click on the fx icon and search/select
If you don't see the Data Analysis option in the Data ribbon, what do you need to do?
Enable the Add-in in Excel
Joe is doing an analysis of data for his Economics 104 class. He has the value of the foreign direct investment and political stability of one country. What could he learn about this relationship from the Pearson Coefficient?
How strong the relationship is
Which of the following is TRUE about the coefficient of determination?
It is a quantity that indicates how well a statistical model fits a data set.
Mary is studying the relationship between hours slept and number of puzzles solved. She collects the following data where the x-value is hours slept and the y-value is puzzles solved: (5,3), (7,8), (4,6). Mary wants to calculate a Pearson coefficient, so she begins by organizing her data as shown below. Which of the following best describes the mistake that Mary made?
Mary did not keep each subject's results together.
What is it called when dependent variables and independent variables in a data set either increase or decrease opposite from one another?
Negative correlation
In order to find a Pearson correlation, the distribution of the data must be _____.
Normal
Zoe needs to analyze the strength of the relationship between two variables. What is the correct name for the test she needs to conduct?
Pearson R
A portfolio of stocks has a correlation to a global energy index of +0.85. If you desire risk reduction in the portfolio, what is the best course of action?
Sell some of your energy stocks and purchase other unrelated assets.
Susan conducts a study and is able to make a scatterplot from the data she gathers. Susan's study is chosen to be published in a scientific journal, but does not include her scatterplot. Which of the following explains why Susan chooses not to include her scatterplot in the scientific journal?
Susan does not include her scatterplot because the coefficient correlation is sufficient.
How are the coefficient of determination and the correlation coefficient related?
The coefficient of determination is the square of the correlation coefficient.
The price of a small company's stock correlated to a large capital index measurement is -0.02. What of the following is best understood from this fact?
The company stock price has a random statistical relationship to the index.
Which of the following best describes why the correlation coefficient is important?
The correlation coefficient describes the relationship between the two variables.
Which of the following is true concerning the correlation coefficient?
The correlation coefficient must be between -1 and 1.
The correlation coefficient explains which of the following?
The strength and direction of the relationship between two variables.
Every time the Federal Reserve bank decreases the prime lending rate by 1%, automobile sales go up by 2%. Which of the following is the best statement to make regarding the correlation of these values?
The two actions appear to be negatively correlated.
There is a correlation coefficient between bean bag sales and drunk driving citations (0.86). What does this mean?
There is a strong relationship between the variables
The correlation coefficient between the number of girls passing in Physics at grade 9 and the number of girls passing in Physics at grade 11 is 0. Identify the correct statement for the above.
There is no correlation between the number of girls passing in Physics at grade 9 and the number of girls passing in Physics at grade 11
In order to use the CORREL function in Excel, what is needed?
Two arrays of numeric data
Find the correlation coefficient that exist between the two variables X and Y as given by the following coordinates. (1,2) (2,1) (2,6) (3,1)
Work out values for X^2, Y^2 and XY. Also obtain the summations for X (=8), Y(=10), X^2(=18), Y^2(=42) and XY(=19). n = 4 Then use the equation for calculating r. r = [4(19) - (8)(10)] / {√ [4(18) - (8)^2][4(42) - (10)^2]} r = -4 / √544 r = -0.17
Which of the following is TRUE about the correlation coefficient?
a measure of the statistical relationship between x and y.
What does r^2 represent?
coefficient of determination
What is a condition or piece of data in an experiment that can be controlled or changed?
independent variable
A company has to pay more in tariffs each year, and passes all of the added cost along to its customers as part of the retail sales price. If everything else stays exactly the same, what can be said about the correlation of tariffs and higher prices, as measured by that company?
the correlation of tariffs and higher prices will be positive.