Microeconomics University of Memphis Meritan October & November Behaviors HW Please do not pick up this assignment if you cannot complete it in the time fr

Microeconomics University of Memphis Meritan October & November Behaviors HW Please do not pick up this assignment if you cannot complete it in the time frame needed to be or if you cannot do the work. Thank you!I have uploaded the instructions for the assignment. The paper has to be 2 pages doubled spaced size 12 Times New Roman font. Proper grammar and complete sentences are a must along with any references found to be cited in APA format. The information that I have placed in Parenthesis and Bold is my information that is needed for that portion of the paper in the instructions of the assignment. It is a lot of information that I have given you but I want to make sure everything is there and correct. Please read EVERYTHING carefully!Thank you! Final Project ASSIGNMENT:
Write a brief (2 page) paper which includes a regression analysis that is related to the company
where you are employed or your industry. (The company that I am employed at is Meritan) (I
am the Foster Care Recruiter/Trainer. I teach the foster parents and potential foster
parents classes that will guide them when becoming a foster parent: For example: Effective
Discipline, Cultural Awareness, and CPR/First Aid) I also go out and recruit potential
foster parent(s) so their home can be certified to foster children. I write the home studies
and I am a foster parent support person.
REQUIREMENTS: You are expected to find data related to your company, perform either a
simple or multiple regression analysis of this data, and write a summary of your findings. You
need to find data on two variables (My two variables are: A foster parent analyzed the
relationship between a Level 1, Level 2, and Level 3 foster children in the home and the
average number of weekly behaviors between each of them) which may be related. (The
foster parent has a Level 1, Level 2, and Level 3 child in her home). Your paper will
investigate the strength of this relationship using regression. You will need to make sure your
company authorizes the use of this data. Your data and paper will not be made public, but please
respect any privacy laws of your company. Ideally, the more “observations” or data points the
better. For instance, if you are looking at data on the number of customers and average wait time,
it would be better to have 200 different rows of data in your dataset than 30, but ideally you
would have at least 30.
• Determine which variables of interest might be available to you at your workplace. Examples
of past projects include:
o A pharmacist analyzed the relationship between the number of z-pack prescriptions and the
average daily temperature over the past two months.
o An administrative assistant at a hospital analyzed the relationship between patient wait time
and number of available staff members.
o A Jackson Energy Authority employee analyzed the relationship between temperature and
number of service calls.
o A graduate assistant for the basketball team evaluated the relationship between ticket sales and
ranking.
(I have chosen: A foster parent analyzed the relationship between a Level 1, Level 2, and
Level 3 foster children in the home and the average number of weekly behaviors) because
the agency that I work for is a foster care agency.
• You must identify which variables you intend to analyze
You must provide citations for sources if you use them and indicate any material that is directly
copied from a particular source.
Your paper will be graded for content, organization, and clarity (clear ideas, logical flow of
paragraphs, clear discussion of results), and mechanics (grammar, sentence structure). Your
presentation will be graded for organization, professionalism, eye contact, and clarity.
No cover pages please. Simply put your name and a title for your paper on the first page. (No
other information such as date, class, etc. please.)
• Your paper should not be shorter than 2 double-spaced pages, with one-inch margins and 12
point Times New Roman font. It is acceptable to write slightly beyond two pages, but at most
two and a half pages. Any tables or graphs you include do NOT count towards the 2-page
requirement.
Keep in mind that you will need at least two variables and that you will be investigating the
relationship between these variables. If additional variables are available and you would like to
run a multiple regression instead of a simple regression, that is acceptable, but is not required.
• In your paper, you might discuss why the variables you’ve selected are of interest, what
relationship they have to the work that you do for your company, and how your company might
use the results of your analysis.
• You might also include a brief description of your company, where it is located, and what
position you hold. If appropriate, you may include a very brief history of the company. Do NOT
do this in an effort to take up space. (This is the information about the company I work for:
About Us:
We serve people.
Meritan staff are experts in child & adult support services.
Our mobile professional & personal care staff can assist,
make connections, build families or generate second careers for seniors.
Whether it is…
aging independence, physical recovery
living with intellectual disabilities
temporary state foster care
training for a second career for seniors
private adoption home studies
or simply making valuable connections during a crisis
Meritan is there.
(This is the department I worked underneath at Meritan: Foster Care)
We aim to protect them from less than a full life, but we cannot achieve our goals alone. At a
Specialized Foster Care home, children receive so much more than the necessary medical or
behavioral treatment. Every day they are exposed to basic human warmth and affection, allowing
them to grow strong through experiences that most people take for granted. This warmth and
affection plays a critical role in their full recovery.
Training is also a key to the success of a placement in the modern foster home. Meritan provides
support and instruction to foster parents from trained professionals. Our staff is always available
to answer questions and to respond immediately to any concerns from the foster family or
children.
We specialize in medical and therapeutic support, keeping families together, and safe households
for children and pregnant teens. Meritan provides this program in Arkansas, Georgia, and
Tennessee (I am working in Tennessee). It is also available in Mississippi under the name
Apelah.
• As you analyze your variables, you might indicate what relationship you expect to see between
the variables prior to running the regression. If you have data for several months or years, you
might discuss the changes that you see over time in the data and why those may exist.
• Your paper should properly analyze your regression results using the examples provided in
class.
• Review the regression explanation included in Module 6 if you need help interpreting your
output. (I have uploaded Module 6)
October 2019
Week 1
Week 2
Week 3
Week 4
LEVEL 1 (L1) Child
0 behaviors
0 behaviors
2 behaviors
3 behaviors
LEVEL 2 (L2) Child
2 behaviors
6 behaviors
6 behaviors
0 behaviors
LEVEL 3 (L3) Child
6 behaviors
3 behaviors
3 behaviors
3 behaviors
Level 1 Child- A child coming into custody for the first time or has been adandon by the parent(s)
Level 2 Child- A child coming into custody due to abuse such as but not limited to: Physical or sexual abuse, or due to neglect
Level 3 Child- A child coming into custody due to servere mental health issues/behaviors or a Juvenile Justice youth
Level 3 is our highest level
buse, or due to neglect
Justice youth
Novemeber 2019
Week 1
Week 2
Week 3
Week 4
Level 1 (L1) Child
1 behavior
1 behavior
3 behaviors
1 behavior
Level 2 (L2) Child
4 behaviors
4 behaviors
2 behaviors
0 behviors
Level 3 (L3) Child
4 behaviors
2 behaviors
0 behaviors
3 behaviors
Demand Estimation
 Regression – the use of data on economic variables
Regression Estimation
to determine mathematical relationship between
variables
= 180 – 10 – 0.2 + 10
CHAPTER 4
 _____________– the coefficients in the equation
 Regression analysis has two goals:


1
Estimation of parameter values
Tests for statistical significance
2
Goals
Simple Regression
 To learn how to perform a regression
 Examine the relationship between Y and X.
 To learn how to interpret a regression
 Simple linear regression analysis takes data on Y

and X and provides a linear equation describing the
relationship:
Focus on the basics, not the complex math
Dependent
Variable: what
we are trying to
explain
Y = a + bX
Intercept:
The value
of Y when
X=0
3
Slope parameter
(or coefficient):
rate of change in
Y as X changes
Independent
Variable: a
variable that
we believe
impacts Y
4
1
Simple Regression
College GPA
3
3.4
3
3.5
3.6
3
2.7
2.7
2.7
3.8
2.8
2.9
3
2.9
3.3
2.6
.
.
.
 Example: the relationship between college GPA and
ACT score for college students
= +
Dependent
Variable: what
we are trying to Intercept:
The value
explain
of Y when
X=0
Slope parameter
(or coefficient):
rate of change in
Y as X changes
Independent
Variable: a
variable that
we believe
impacts Y
5
ACT
21
24
26
27
28
25
25
22
21
27
19
22
23
29
25
21
.
.
.
4.5
4
3.5
3
College GPA
Simple Regression
2.5
2
1.5
1
0.5
0
0
5
10
15
20
25
30
35
ACT
6
Results of Simple Regression in Excel
Simple Regression
SUMMARY OUTPUT
= 2.403 + 0.027
Regression Statistics
Multiple R
0.207
R Square
0.043
Adjusted R Square
0.036
Standard Error
0.366
Observations
 We use the parameters estimated by the regression
to form the regression equation.
141.000
ANOVA
df
Regression
SS
F
0.830
0.830
139.000
18.577
0.134
Total
140.000
19.406
Coefficients
7
MS
1.000
Residual
Standard Error
t Stat
Significance F
6.207
P-value
0.014
Lower 95%
Upper 95%
Intercept
2.403
0.264
9.095
0.000
1.881
2.925
ACT
0.027
0.011
2.491
0.014
0.006
0.049
8
2
Multiple Regression
 Multiple regression: regression with
_________________ independent variable
Results of Multiple Regression in Excel
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.354
R Square
0.125
Adjusted R Square
= + + Z
0.113
Standard Error
Observations
0.351
141.000
ANOVA
= + + skipped
df
Regression
Residual
Total
SS
1.217
0.123
140.000
Significance F
9.900
0.000
19.406
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
2.404
0.253
9.485
0.000
1.903
2.905
ACT
0.031
0.010
2.997
0.003
0.011
0.052
-0.099
0.027
-3.613
0.000
-0.153
-0.045
skipped
10
Interpreting the Linear Regression Equation
College GPA = 2.404 + 0.031ACT − 0.099skipped


11
F
2.435
16.971
Coefficients
9
MS
2.000
138.000
Plug different values for ACT and skipped in to estimate the expected
value of CollegeGPA
Example: CollegeGPA = 2.404 + 0.031(27) – 0.099(2)
= 3.04
Use the slope parameter to interpret how a one unit change in the
variables changes College GPA
Example:
 0.031 is the coefficient on ACT. Scoring one point higher on the ACT
increases CollegeGPA by 0.031 points.
 -0.099 is the coefficient on skipped. Skipping one more day of class
decreases a student’s GPA by 0.099 points.
Testing for Statistical Significance
Statistically significant results are those that DO NOT occur by
chance.
College GPA = 2.404 + 0.031ACT − 0.099skipped
 a, b, and c are only estimates of the actual parameter values.
 We can use statistical analysis to determine the accuracy of
our estimates both for our estimated parameter values and
for the overall regression.
 Tests for Statistical Significance include:


Evaluating the statistical significance of one or more parameters.
Two measures we can use are t-statistics and p-values.
Evaluating the precision with which the overall regression line fits
the data. Two measures we can use are R-square and Significance F.
12
3
Results of Regression Analysis
Interpreting Regression Output – Evaluating the Parameters
First, we are interested in determining if the parameter estimates are
statistically significant – in other words, are they far enough away from 0?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.354
R Square
0.125
Adjusted R Square
If we find that the slope of the regression line is significantly different from
zero, we will conclude that there is a significant relationship between the
independent and dependent variables.
0.113
Standard Error
Observations
CollegeGPA = a+ 0ACT+ 0skipped
0.351
141.000
Hypothesis Testing:
ANOVA
df
Regression
SS
2.000
MS
1.217
0.123
Residual
138.000
16.971
Total
140.000
19.406
Coefficients
F
2.435
Standard Error
t Stat
Significance F
9.900
P-value
Lower 95%
Upper 95%
Intercept
2.404
0.253
9.485
0.000
1.903
2.905
ACT
0.031
0.010
2.997
0.003
0.011
0.052
-0.099
0.027
-3.613
0.000
-0.153
-0.045
skipped
1)
2)
3)
4)
5)
6)
0.000
13
14
Testing for Statistical Significance of Parameters
1) Specify the significance level – the probability of
Testing for Statistical Significance of Parameters
2) Calculate the test statistic
finding a parameter to be significant when it isn’t



Chosen by the researcher
Significance level is our tolerance for obtaining a result which
indicates that the coefficient does have an impact on the
dependent variable when in reality it doesn’t impact the
dependent variable.
the lower the significance level, the more confident we are that
our test will correctly indicate a lack of significance.

Calculated as the parameter estimate (denoted as b̂ ) divided by its
standard error

For our example:
0.031
= 0.010 = 2.997
0.10 (90% confident)
0.05 (95% confident)
0.01 (99% confident)
15
Specify the Significance Level
Calculate the Test Statistic
Determine the Degrees of Freedom
Find the Critical Value
Compare Critical Value to Test Statistic
Find more precise significance level with
the P-value
Coefficients Standard Error
Intercept
t Stat
P-value
9.485
0.000
2.404
0.253
ACT
0.031
0.010
2.997
0.003
skipped
-0.099
0.027
-3.613
0.000
16
4
Testing for Statistical Significance of Parameters
3) Determine the degrees of freedom
For a t-test, degrees of freedom = −
where n = number of _____________ in sample
where k = number of __________ being estimated
Testing for Statistical Significance of Parameters
4) Find the critical value
For a t-test, critical values are found in t-tables.
For our example: = + + skipped
Regression Statistics
Multiple R
0.354
R Square
0.125
Adjusted R Square
0.113
Standard Error
Observations
17
− = 141 – 3 = 138
0.351
141.000
18
Testing for Statistical Significance of Parameters
4) Find the critical value
For a t-test, critical values are found in t-tables.
For our example:
Significance level = 0.05
Degrees of freedom = 138
Critical Value = 1.960
RULE: If (absolute value) of test statistic > critical value
then the estimated parameter is statistically different than 0
and thus is statistically significant.
19
20
5
Testing for Statistical Significance of Parameters
Interpreting Regression Output – Evaluating the Coefficients
6) Find a more precise significance level with the Pvalue
5) Compare Critical Value to Test Statistic
 The P-value tells you the exact significance level for the t-statistic;
RULE: If (absolute value) of test statistic > critical value
then the estimated parameter is statistically different than 0
and thus is statistically significant.
For our example:
it tells you the exact probability that you will find a parameter to
be significant when it isn’t
 For our example: P-value for the ACT coefficient is 0.003 which
indicates that the estimated coefficient is highly statistically
significant (less than 0.3%).
 This means that there is only a very, very, tiny chance that ACT
does not affect College GPA.
Critical Value = 1.960
Test Statistic = 2.997
Since 2.997> 1.96, ACT is a statistically significant variable
at the 5% level. Thus, there is only a 5% chance that ACT
does not impact College GPA.
21
Coefficients Standard Error
 Earlier we said……..
 Tests for Statistical Significance include:


0.253
9.485
0.000
0.031
0.010
2.997
0.003
skipped
-0.099
0.027
-3.613
0.000
Interpreting Regression Output – Evaluating the Overall
Fit of the Regression Line
Evaluating the statistical significance of one or more parameters. Two
measures we can use are t-statistics and p-values.
Evaluating the precision with which the overall regression line fits the data.
Two measures we can use are R-square, F statistic and Significance F.
1) Evaluate the R-square: the fraction of the
variation in the dependent variable that is explained by
the regression equation.

Rule of thumb:
The closer R-square is to 1, the more Y is related to X and Z, and
the better the overall fit of the estimated regression line to the data
and the higher the correlation between the dependent and
independent variables.
 The closer R-square is to 0, the less Y is related to X and Z and the
worse the overall fit of the estimated regression line to the data
and the lower the correlation between the dependent and
independent variables.

Testing for Significance of the Regression Equation:
23
P-value
2.404
ACT
22
Statistical Significance
1)
2)
3)
4)
5)
6)
t Stat
Intercept
Evaluate R-square
Locate the Test Statistic (F-stat)
Specify the Significance Level and Determine the Degrees of Freedom
Find the Critical Value
Compare Critical Value to Test Statistic
Find more precise significance level with the Significance F
24
6
Interpreting Regression Output – Evaluating the Overall
Fit of the Regression Line
Results of Regression Analysis
SUMMARY OUTPUT
R Square:
Regression Statistics
Multiple R
0.354
R Square
0.125
Adjusted R Square
0.113
Standard Error
0.351
Observations

141.000

ANOVA
df
Regression
Residual
Total
SS
MS
F
2.000
2.435
1.217
138.000
16.971
0.123
140.000
Coefficients
Significance F
9.900
0.000
19.406
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
2.404
0.253
9.485
0.000
1.903
2.905
ACT
0.031
0.010
2.997
0.003
0.011
0.052
-0.099
0.027
-3.613
0.000
-0.153
-0.045
skipped
25
26
Interpreting Regression Output – Evaluating the Overall
Fit of the Regression Line
Interpreting Regression Output – Evaluating the Overall
Fit of the Regression Line
2) Locate the test statistic (F-stat)
3) Specify the significance level and
determine degrees of freedom
Recall: the t-stat was used to test whether one of the parameters was
significantly different from zero.
The F-stat will be used to test whether all the parameters are
significantly different from zero.
 As a group do the parameters have an impact on the dependent
variable?
F
9.900
c
27
Here, 12.5% of the variation in College GPA is explained by the
regression equation.
Note: There is no universal rule for determining how “high” Rsquare should be to determine a good fit. Even models with a
low R-square can be used to evaluate the impact of particular
coefficients on the dependent variable.
Significance level – 0.05
For an F-test, two separate degrees of freedom calculations are needed
1) − 1
2) −
where n = number of observations in sample
where k = number of parameters being estimated
Significance F
−1=3–1=2
− = 141 – 3 = 138
0.000
28
7
Interpreting Regression Output – Evaluating the Overall
Fit of the Regression Line
4) Find the Critical Value
For an F-test, critical values are found in F-tables.
29
30
Interpreting Regression Output – Evaluating the Overall
Fit of the Regression Line
4) Find the Critical Value
Interpreting Regression Output – Evaluating the Overall
Fit of the Regression Line
5) Compare Critical Value to Test Statistic
For an F-test, critical values are found in F-tables.
In our book, the F-table is on pages 703 and 704.
−1=3–1=2
− = 141 – 3 = 138
Critical Value = 2.99
31
RULE: If the test statistic > critical value
then the regression equation (the parameters as a group) is
statistically different than 0 and thus is statistically
significant.
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