Statistics week Five
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week_five_statistics.docxAshford 6: - Week 5 (May 19 - May 25)
Overview
|
Assignment |
Due Date |
Format |
Grading Percent |
|
Correlation |
Day 3 (1st post) |
Discussion |
3 |
|
Regression |
Day 3 (1st post) |
Discussion |
3 |
|
Problem Set Week 5 |
Day 7 |
Assignment |
8 |
|
Final Paper |
Day 7 |
Assignment |
14 |
Note: The online classroom is designed to time students out after 90 minutes of inactivity. Because of this, we strongly suggest that you compose your work in a word processing program and copy and paste it into the discussion post when you are ready to submit it.
Learning Outcomes This week students will:
1. Perform a simple regression.
2. Perform a multiple regression.
3. Interpret the results of simple and multiple regressions.
4. Analyze correlation coefficients.
5. Create a report identifying possible uses of statistical analysis in work or other settings.
Introduction
In Week Five, the focus will be on correlations and single and multiple regressions. Predicting the future is a central requirement in business decision making. Managers use existing data to predict the future values of other variables of interest. For example, marketing data is used to predict future sales. Chapter 8 examines the correlation between two variables. The sign of the correlation coefficient indicates the direction of the relationship. Positive correlations indicate that as the values in one variable increase, the values in the other will do the same. Negative correlations indicate that as one increases, the other decreases. In Chapter 9, students will examine how to conduct a simple and multiple regression analysis and apply it to the business environment. The idea that variables correlate because they share common information is a powerful concept to be examined this week.
Required Resources Required Text
1. Read the following chapters from Statistics for Managers:
a. Chapter 8: Correlation
b. Chapter 9: Simple Regression: Predicting One Variable From Another
c. Chapter 10: Multiple Regression: Using More Than One Predictor
d. Chapter 11: Confidence Intervals
Recommended Resources Articles
1. Hall, S. (2013, June 8). How to use multiple regression in Excel . eHow. Retrieved from http://www.ehow.com/how_5768074_use-multiple-regression-excel.html
2. Koltow, D. (n.d.). How to calculate linear regression using Excel . eHow. Retrieved from http://www.ehow.com/how_8429122_calculate-linear-regression-using-excel.html
Multimedia
1. Khan Academy. (Producer). Regression [Video files]. Retrieved from https://www.khanacademy.org/math/probability/regression.
2. Meridian Education Corporation & Advanced Productions (Producers). (2001). Drinking and driving: A crash course [Video File]. Retrieved from the Films On Demand database.
3. Surgey, P. (Producer). (1995). The passionate statistician: Florence Nightingale [Video File]. Retrieved from the Films On Demand database.
Discussions To participate in the following discussions, go to this week's Discussion link in the left navigation.
1. Correlation
What results in your departments seem to be correlated or related (either causal or not) to other activities? How could you verify this? What are the managerial implications of a correlation between these variables?
Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by explaining whether or not you think that there is a relationship between the variables discussed.
2. Regression
At times we can generate a regression equation to explain outcomes. For example, an employee’s salary can often be explained by their pay grade, appraisal rating, education level, etc. What variables might explain or predict an outcome in your department or life? If you generated a regression equation, how would you interpret it and the residuals from it?
Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on how this information might be used to make business decisions.
Assignment To complete the following assignment, go to this week's Assignment link in the left navigation. Problem Set Week Five
Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Employee Salary Data Set and the Week 5 assignment sheet.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
Final Paper To complete the following final paper, go to this week's Final Paper link in the left navigation.
The Final Paper provides you with an opportunity to integrate and reflect on what you have learned during the class. The question to address is: “What have you learned about statistics?” In developing your responses, consider – at a minimum – and discuss the application of each of the course elements in analyzing and making decisions about data (counts and/or measurements). The course elements include:
· Descriptive statistics
· Inferential statistics
· Hypothesis development and testing
· Selection of appropriate statistical tests
· Evaluating statistical results.
Writing the Final Paper The Final Paper:
1. Must be three to- five double-spaced pages in length, and formatted according to APA style as outlined in the Ashford Writing Center.
2. Must include a title page with the following:
1. Title of paper
2. Student’s name
3. Course name and number
4. Instructor’s name
5. Date submitted
3. Must begin with an introductory paragraph that has a succinct thesis statement.
4. Must address the topic of the paper with critical thought.
5. Must end with a conclusion that reaffirms your thesis.
6. Must use at least three scholarly sources, in addition to the text.
7. Must document all sources in APA style, as outlined in the Ashford Writing Center.
8. Must include a separate reference page, formatted according to APA style as outlined in the Ashford Writing Center.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
Ashford 6: - Week 5 - Instructor Guidance
Weekly Overview
The Covariance
The covariance measures the strength of the linear relationship between two numerical variables (X & Y)
The covariance only concerned with the strength of the relationship
There is no causal effect is implied.
cov(X,Y) > 0 X and Y tend to move in the same direction
cov(X,Y) < 0 X and Y tend to move in opposite directions
cov(X,Y) = 0 X and Y are independent
The covariance has a major flaw:
It is not possible to determine the relative strength of the relationship from the size of the covariance
Coefficient of Correlation
It measures the relative strength of the linear relationship between two numerical variables
Sample coefficient of correlation:
r= Sx = Sy =
The population coefficient of correlation is referred as ρ.
The sample coefficient of correlation is referred to as r.
Either ρ or r has the following features:
Unit free
Ranges between –1 and 1
The closer to –1, the stronger the negative linear relationship
The closer to 1, the stronger the positive linear relationship
The closer to 0, the weaker the linear relationship.
During this week, you’ll learn
How to use regression analysis to predict the value of a dependent variable based on an independent variable
The meaning of the regression coefficients b0 and b1
How to evaluate the assumptions of regression analysis and know what to do if the assumptions are violated
To make inferences about the slope and correlation coefficient
To estimate mean values and predict individual values
· How to develop a multiple regression model
· How to interpret the regression coefficients
· How to determine which independent variables to include in the regression model
· How to determine which independent variables are more important in predicting a dependent variable
· How to use categorical variables in a regression model
Regression Basics
Regression analysis is used to:
Predict the value of a dependent variable based on the value of at least one independent variable
Explain the impact of changes in an independent variable on the dependent variable
Simple Least liner Regression
A single numerical independent variable, X, is used to predict the numerical dependent variable Y, such as using the size of a store to predict the annual sales of the store.
Only one independent variable, X
Relationship between X and Y is described by a linear function
Changes in Y are assumed to be related to changes in X
Interpreting a
a is the estimated mean value of Y when the value of X is zero (if X = 0 is in the range of observed X values)
Interpreting of b
b estimates the change in the mean value of Y as a result of a one-unit increase in X
Multiple Regression Models
Multiple regression models use two or more independent variables to predict the value of dependent variable.
Assumption of Regression
The four assumption of regression are linearity, independence of errors, normality of error and equal variance. Linearity states that the relationship between variables is linear. Independence of errors requires that the errors are independent of one another. This assumption is particularly important when data are collected over a period of time. In such situations, the errors for a specific time period are sometimes correlated with those of the previous time period. Normality requires that the errors are normally distributed at the each value of X. Equal variance requires that the variances of the errors are constant for all values of X. That is the variability of Y values is the same when X is a low value as when X is a high value. The equal variance assumption is important when making inferences about a and b.
Discussions
You need to review correlation and regression before you answer the questions.
Assignment
1. You need to use ToolPak: choose correlation function. The result is a table of correlations. When you choose the data range, you should leave out non-numeric columns. An example of Excel output is on page 220. However, there are only two columns of data in the example.
2. The results are shown; you just need to interpret the results. An example is on page 278.
3. This is similar to #2 except this one is “Compa” instead of “Sal”. The Excel output format is the same. An example is on page 278.
Ashford 6: - Week 5 - Discussion 1
Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.
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|
|
Correlation |
What results in your departments seem to be correlated or related to other activities? How could you verify this? Create a null and alternate hypothesis for one of these issues. What are the managerial implications of a correlation between these variables?
Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by explaining whether or not you think that there is a relationship between the variables discussed.
Ashford 6: - Week 5 - Discussion 2
Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.
|
|
|
Regression |
At times we can generate a regression equation to explain outcomes. For example, an employee’s salary can often be explained by their pay grade, appraisal rating, education level, etc. What variables might explain or predict an outcome in your department or life? If you generated a regression equation, how would you interpret it and the residuals from it?
Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on how this information might be used to make business decisions.
Ashford 6: - Week 5 - Assignment
Problem Set Week Five Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations. All statistical calculations will use the Employee Salary Data Set and the Week 5 assignment sheet.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
Ashford 6: - Week 5 - Final Paper
Final Paper The Final Paper provides you with an opportunity to integrate and reflect on what you have learned during the class. The question to address is: “What have you learned about statistics?” In developing your responses, consider – at a minimum – and discuss the application of each of the course elements in analyzing and making decisions about data (counts and/or measurements). The course elements include:
· Descriptive statistics
· Inferential statistics
· Hypothesis development and testing
· Selection of appropriate statistical tests
· Evaluating statistical results.
Writing the Final Paper The Final Paper:
1. Must be three to- five double-spaced pages in length, and formatted according to APA style as outlined in the Ashford Writing Center.
2. Must include a title page with the following:
a. Title of paper
b. Student’s name
c. Course name and number
d. Instructor’s name
e. Date submitted
3. Must begin with an introductory paragraph that has a succinct thesis statement.
4. Must address the topic of the paper with critical thought.
5. Must end with a conclusion that reaffirms your thesis.
6. Must use at least three scholarly sources, in addition to the text.
7. Must document all sources in APA style, as outlined in the Ashford Writing Center.
8. Must include a separate reference page, formatted according to APA style as outlined in the Ashford Writing Center.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
