Quantitative Methods and Analysis: Unit 5

Welcome Info

Welcome to Unit 5!

Can you believe it is the last week of the course already? It is amazing how fast five weeks can fly!

Before we continue, I want to thank you for five great weeks! I wish you all the best of luck in your future studies and careers. I hope you will be able to look back on the last five weeks and say that you have learned something very valuable.

This week we will explore correlations. This is a very valualbe concept that permits us to identify relationships between variables. Determing that two variables are related gives us the opportunity to make predictions about the future based on what we know about the past. This is a very powerful tool!

You will find the same format as in last week’s Try This! Document. In each Green Tab, you will find information about the task you should complete. In each Red Tab, you will find the solutions.

This process will permit you to check your work and ensure that you can complete the necessary tasks in order to learn the concept you required to use for your last IP.

If your solution does not agree with the "answer" provided, please feel free to contact me at:

[email protected]

PLEASE NOTE: This resource is ONLY applicable to those students who use Microsoft Excel. Whether you use Microsoft or have a Mac, you still need to activate the processing software, such as the Data Analysis Toolpak or the StatPlus from AnalystSoft. Please review the information from the link in the Unit 1 Assignment List for more details.

mailto:[email protected]

Sample Data

Animal type	Visit Code	Gender	Weight (lbs)	Age (years)	Cost		Key
0	1	0	12.3	4	$125		Animal Type	0	Cat
0	2	0	14.3	2	$85			1	Dog
0	1	1	8.9	3	$109			2	Bird
0	1	0	7.3	0.5	$99			3	Other
0	3	1	10.3	9	$250		Visit Code	1	Routine check up
1	1	1	12.3	9	$150			2	Illness
1	2	0	78.2	12	$212			3	Emergency
1	2	1	50.4	8	$73		Gender	0	Male
1	1	1	33.2	2	$90			1	Female
1	3	0	89	3	$459
1	1	0	5.4	1	$153
2	1	1	2.3	2	$90
2	1	1	3.1	1	$85
3	2	1	3.4	2	$74
2	1	0	2.2	3	$48
1	2	1	102.3	5	$67
1	2	1	32.1	6	$109
1	1	0	67.2	2	$88
2	1	0	3.4	4	$40
2	2	1	1.2	1	$72
1	3	1	8.9	8	$280
SAMPLE DATA WARNING
This is the sample data set you will be using to demonstrate several concepts for the practice exercises. You will NOT be using this data set for any of your IPs in the course. This is for practice ONLY! For the course IPs, you will be using the data set that is available in the Unit 1 IP Assignment List, located via a link titled 2003 Excel Data Set and Data Set Key. Remember that you should use ONLY the current DataSet for the current course for the IP assignments. This sample data will be used for the “Try This” worksheet assignments for practice exercises. These are opportunities for you to learn the process before you complete your actual IP work. This is NOT a requirement. It is simply an opportunity to improve by learning the steps.
Sample Data Information
The data was collected one day from a veterinarian office. Twenty-one animals entered the practice for treatment of some kind. The Animal Type, Reason for Visit, Gender, Weight, Age and Cost of Visit were recorded. For ease of analysis, the first three variables were given a code (computers deal better with numbers). To assist you in the analysis, the qualitative variables’ labels were colored in RED. The quantitative variables’ labels were colored in GREEN.

Creating Scatter Plots

A graph can be a powerful visual depicting the relationship between variables.

In the live chat session we explored the various relationships that can be viewed on a graph. We can determine the direction of the relationship (positive or negative) and the strength (strong, moderate, weak or none). I encourage you to view the live chat for more details.

Before we start this process please view the following video:

Creating a scatter plot

Now try creating a scatter plot to show the relationship between weight (independent variable) and cost (dependent variable).

I weigh 78 pounds. I wonder how much a vet visit will cost??

http://youtu.be/xPcssgiX5Mk

Scatter Plot Solution

Your set up should look like this:
Independent	Dependent
Weight (lbs)	Cost
12.3	$125
14.3	$85
8.9	$109
7.3	$99
10.3	$250
12.3	$150
78.2	$212
50.4	$73
33.2	$90
89	$459
5.4	$153
2.3	$90
3.1	$85
3.4	$74
2.2	$48
102.3	$67
32.1	$109
67.2	$88
3.4	$40
1.2	$72
8.9	$280
From this graph we can see the relationship is positive. The line increases from left to right. This indicates that as weight increases, so does cost.

Cost vs. Weight

Cost 12.3 14.3 8.9 7.3 10.3 12.3 78.2 50.4 33.200000000000003 89 5.4 2.2999999999999998 3.1 3.4 2.2000000000000002 102.3 32.1 67.2 3.4 1.2 8.9 125 85 109 99 250 150 212 73 90 459 153 90 85 74 48 67 109 88 40 72 280

Weight

Cost

Regression Output

Next, we want to find more information about the relationship between weight and cost. We will do this by finding the full regression output from the data analysis tool pack in Excel. This will give us a slope (rate of change) and intercept (y-value if X=0) for each variable pairing. We can use the slope and intercept to write an equation in the form y=intercept+slope(x). Once you have an equation, it can be used to make predictions.

To get started, please view this video:

Regression output in excel

**You must have the data analysis tool pack running to create this analysis***

Now try it yourself! Create the regression output for weight (x) and cost (y).

http://youtu.be/Uxu-_wjs6wM

Regression Solution

Yoru output should look like this:
SUMMARY OUTPUT
Regression Statistics
Multiple R	0.418893
R Square	0.175471345
Adjusted R Square	0.129664198
Standard Error	87.97845064
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	29650.06001	29650.06	3.830654	0.066015
Residual	18	139323.74	7740.208
Total	19	168973.8
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	91.09347491	25.84516081	3.524585	0.002421	36.79481	145.3921	36.79481	145.3921
Weight (lbs)	1.217762624	0.622194491	1.957206	0.066015	-0.08942	2.524945	-0.08942	2.524945
From this, we can seek the intercept is 91.09, which means that a dog weighing 0 pounds will cost about $91.09.
**Note the intercept interpetation may not always make sense**
You can also see the slope is 1.21. That means that every pound of body weight increases the cost by $1.22.
An equation can be written as y=91.09 + 1.22x
This equation can be used to make predictions. Abbey, the dog from the previous tab, weighs 78 pounds. We could predict her vet bill by filling her weight in for x.
y-91.09+1.22(78) = 186.25
The r-squred value also indicates the strength of the relationship. The closer to 1, the stronger the relationship between the two variables.
When comparing mutliple analyses, keep in mind that the stronger the r-squared value is, the stronger the relationship is and the more accurate predictions can be made.

Your IP Checklist

HIGH FIVE!!
You have completed all sample exercises and are now ready to start your last IP.
To help you get started, here is a checklist of items that need to be completed.
Completed?		Area
		Download current session data set
		This is the same one from unit 1
		Download template for IP
		Your entire project should be complete on this template. Do NOT submit your Excel file but copy/paste all information from Excel onto the template
		Failure to use this template will result in an automatic 10-point penalty. DO NOT remove the bold headings.
		Run Regression Analysis for Benefits/Intrinsic Satisfaction
		This must be done in Excel using the Data Analysis Tool Pak
		Copy and paste the entire output onto your paper
		Be sure you use benefits as the x variable and intrinsic as the y variable
		Create a graph for Benefits and Intrinsic
		Be sure your graph contains labels on the x and y axes as well as a title
		Be sure this includes a trendline
		Remember the independent variable goes on the x axis and the dependent variable goes on the y axis
		Run Regression Analysis for Benefits/Extrinsic
		This must be done in Excel using the Data Analysis Tool Pak
		Copy and paste the entire output onto your paper
		Be sure you use Benefits as the x-variable and extrinsic as the Y variable
		Create a graph for Benefits and Extrinsic
		Be sure your graph contains labels on the x and y axes as well as a title
		Be sure this includes a trendline
		Remember the independent variable goes on the x axis and the dependent variable goes on the y axis
		Run Regression Analysis for Benefits/Job Satisfaction
		This must be done in Excel using the Data Analysis Tool Pak
		Copy and paste the entire output onto your paper
		Be sure you use benefits as the X variable and job satisfaction as the Y variable
		Create a graph for Benefits/Job Satisfaction
		Be sure your graph contains labels on the x and y axes as well as a title
		Be sure this includes a trendline
		Remember the independent variable goes on the x axis and the dependent variable goes on the y axis
		Fill in the table of descriptive information
		Type in the information directly onto the template
		Identify the Slope
		Identify the Intercept
		Write an equation
		Identify the r-squared value
		Do not write a +- as that does not make mathematical sense. If the slope is negative, write Y=b-ax for your equation.
		Identify Similarities and Differences
		Review the Excel output and graphs
		Identify at least one similarity and one difference
		BE SPECIFIC
Be sure that you also take advantage of the Fundamentals of Statistics Lab for lectures, demonstrations and other materials. You may access the lab by clicking on the Learning Center, the Learning Labs, the Fundamentals of Statistics Lab and Live Chat Session to attend live or to review from the chat archives.

DO NOT MAKE THESE ERRORS

Unit 5 Common Errors

There are several common errors students make on the last unit. Be sure to avoid these! Pay careful attention to the following errors that your classmates in the past have made so that you don’t make the same mistakes.

Discussion board

Use of excessive quotes

Explain correlational research in your own words,. Take what you learned through research and put it in your own words

Providing an example

When you provide an example of two variables that may be correlated, one variable must be from our study. Take a look at the Ecel worksheet pertaining to job satisfaction. Which of those nine variables do you think is correlated to a workplace variable? Why?

Length

Your main discussion board post should be at least 300 words long. Show what you know!

Responses to peers

Be sure to respond in the required manner. Pease see the assignment for details.

Individual project

Variable choice

Pay careful attention as to which variable goes where. Remember that benefits is always the x variable or independent variable, while the y or dependent variable is the job satisfaction variable (intrinsic, extrinsic or overall)

Graph labels

Be sure that each graph has a label on the x and y axis as well as a title. This will allow you to clearly identify the graph and all of its aspects. You can add labels and titles under the layout tab in Excel.

Summarizing the results

Write an equation in the form y = b + ax where b is the y-intercept and a is the slope

Do NOT write a + - symbol next to each other. If you have a negative slope, which is possible, ONLY write the—sign so your equation would look like y=b-ax

Summary of results

Be specific when you compare similarities and differences

After identifying the strongest correlation coefficient, explain WHY that is important. How could a manager use these results?

Sources

Be sure to cite resources in text as well as at the end of your paper!