Posted: September 18th, 2022

regression analysis project paper

ProjectPaper xproject xProjectData.xlsx

 regression analysis project paper  

Study of the Age of Art Museums Visitors in the U.S.

Art museums are crucial for conserving culture and history and educating and gathering the community. Museums are places that carry human civilization and are an important part of basic education. Improve the cognitive and aesthetic level of visitors in the development and guidance. However, today art museums are facing the challenge of the multitude of alternatives for entertainment and education, including online streaming, Instagrammable pop-ups, and the easy online accessibility of content previously exclusive to museums.

In additional, museums are economic engines. Before the pandemic, museums support over 726,000 American jobs and contribute $50 billion to the US economy each year. The economic activity of museums generates over $12 billion in tax revenue, one-third of it going to state and local governments. Each job created by the museum sector results in $16,495 in additional tax revenue. The future of museums depends on securing current, but, more importantly, the future visitors. The only way to do this is by understanding the audiences art museums attract as well as the ones they do not. This study is to understand the American visitors of domestic art museums by ago in 1982 to 2019. Therefrom, we can know the potential relationship between age and art museum attendance from this study.

https://www.sciencedirect.com/science/article/abs/pii/S0304422X18300792

I. PROJECT PAPER REQUIREMENTS

A project paper: you will come up with a research question to investigate. You will apply regression analysis, a popular statistical method, to study the potential relationship between three variables. For example, how much does the increase in major greenhouse gases such as carbon dioxide and methane in the atmosphere affect Earth’s temperature? How important are the inflation and unemployment rates in driving interest rate changes? How significant are the gender and age factors in determining the ratings of a TV show? How much do the state of the economy and advertising expenses affect retail sales?

In general, you should select a topic that is neither too technical nor too broad. It would be best to narrow your investigation to a specific (testable) relationship between a few variables. You will need to locate and document your data sources yourself. Data availability should be considered in selecting which research question to pursue. You can use any three data variables you want for your estimated relationship so long as you can justify their relevance for inclusion. There is no restriction on your choice of variables.

After all, all you need is to identify three possibly related variables and gather their data for
your project. You will have one dependent variable (Y) and two explanatory variables (X1 and X2) in your regression model: Y = β0 + β1X1 + β2X2 + ε. You will then estimate the model using Excel’s regression tool and present the results in your paper.

Use publicly available data on the internet (at least 25 observations per variable). Use Excel’s regression tool only. Do not use any other software program.
Page Format: 1.5 spacing, 12 point font size, and one-inch margins.
Page Limit: 4 to 8 pages long, excluding the title page, abstract, tables, and references.

II. ORGANIZATION OF THE PROJECT PAPER

The paper should have a title page with an abstract. Following that, the content of your paper should be presented and organized as follows:

1) Introduction (5 points)

· Identify the purpose of your paper and what research question to investigate.

· Provide some background information related to the topic of your investigation.

· Highlight why the investigation topic is relevant and interesting.

2) Data Description (5 points)

· Describe the sample data set and the type of data you have.

· Explain the data series (Y, X1, and X2) you use and define what they represent and

measure.

· Identify the data source or sources with a Web address for all the data series used in the

study.

3) Statistical Analysis and Results (10 points)

· Explain your data analysis, including the statistical approach (regression method) and the estimated model.

· Tabulate and report the results from your regression analysis, including any additional statistical tests you have conducted.

· Discuss and interpret all your statistical results and findings.

4) Conclusion (5 points)

· Restate the purpose of your study.

· Summarize the key results of your investigation.

· Describe the significance of your findings.

· Outline any limitations of your study


NOTES
:

1. It’s crucial to cite all sources you use to quote, paraphrase, and summarize to avoid plagiarism. For example, the APA citation style is widely used by students, researchers, and professionals in the social and behavioral sciences, natural sciences, business, engineering, and many other fields.

2. No graphs, diagrams, or pictures are needed.

3. You may include a third explanatory variable (X3) in your study if you can provide a reasonable justification for its inclusion.

2

>Sheet

1

Under 18

1

.6

0
0

s

Above 35

0
1

Under 18

1
0

9

Between 18-35

.7

0
0

Above 35

0
1

Under 18

1
0

27

Between 18-35

0
0

Above 35

0
1

Under 18

1
0

Between 18-35

0
0

Regression
2

Above 35

0
1

24

Under 18
29.1
1
0

26

Between 18-35

0
0

Above 35

0
1

Standard Error

Under 18

1
0

22

22222

722524946

23.4721919499

Between 18-35
22.5
0
0

Under 18

2

22222

2

4941

1.1887270328
5.8557174117

Above 35

0
1

Above 35

22222

-4.3557174117
0.3112729672

Under 18

1
0

Between 18-35

0
0

Above 35

0
1

Under 18
26.7
1
0

Between 18-35

0
0

Above 35

0
1

Under 18

1
0

Between 18-35

0
0

Above 35

0
1

https://www.amacad.org/humanities-indicators/public-life/art-museum-attendance#31768
Year Age Level Percentage of Americans Who Visited an Art Museum in the Previous 12 Months Under 18 Above 35 SUMMARY OUTPUT
1982 29.7 0
Between 18-35 24 Regression Statistic
18.7 Multiple R 0.7117058936
1987 29.9 R Square 0.506525

27
26 Adjusted R Square 0.4654023856
23.6 Standard Error 2.3984176883
1992 32.2 Observations
29.1
28.9 ANOVA
1997 29.6 df SS MS F Significance F
26.5 141.7088888889 70.8544444444 12.3173550526 0.000208535
25.6 Residual 138.0577777778 5.7524074074
2002 Total 279.7666666667
24.7
22.5 Coefficients t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
2007 27.6 Intercept 25.122 0.7994725628 31.4234951799 5.19272358118699E-21 23.4721919499 26.7 26.7722524946
3.5222 1.1306 3.1152879213 0.0047113614 1.1887270328 5.8557174117
20.3 -2.02222 1.130624941 -1.7885880179 0.0863130529 -4.3557174117 0.3112729672
2012 26.1
22.0
21.7
2017
24.8
23.5
2019 26.9
25.2
23.1
Note:
Under 18 = Art museum visitors who are under 18 years old (visited outside school)
Between 18-35 = Art museum visitors who are between 18 to 35 years old
Above 35 = Art museum visitors who are above 35 years old

Sheet2

Coefficients

Intercept
25.1222222222
0.7994725628
Under 18

22222

1.130624941

Above 35

1.130624941

=

.

0

27

3.52222

SE
1.13062

24

α
0.05

(from the CV calculator)

rule

if the t-value > the upper CV.

Decision

Copy values from the regression output table:
SE
3.52222
-2.0222222222
Question: Is there significant evidence that art museum attendance rate for American visitor who under 18 years old is higher than the age between 18-35 years old? Use

α 0.05
H0 Ha
Step 1 Hypothesis β1 = 0 β1 > 0
Tested value
Step 2 Sample size
b (β estimate)
t-value 3.1153
Step 3 DF
Type of test upper one tailed
Upper CV 1.7109 (from the CV calculator)
Lower CV n/a
Decision Reject H0 in favor of H

a
Step 4 Reject H0 in favor of Ha at α = 0.05.
Conclusion: There is significant evidence that art museum attendance rate for American visitor who under 18 years old is higher than the age between 18-35 years old (α = 0.05).

Sheet3

Copy values from the regression output table:

Coefficients
SE

Intercept
25.1222222222
0.7994725628

Under 18
3.5222222222
1.130624941

Above 35
-2.0222222222
1.130624941

Question:

H0
Ha

Step 1
Hypothesis

Tested value
0

Step 2
Sample size
27

b (β estimate)
-2.02222

SE
1.13062

t-value

Step 3
DF
24

α
0.05

Type of test

Upper CV
n/a
(from the CV calculator)

Lower CV

(from the CV calculator)

Step 4
Decision

Conclusion:

Is there significant evidence that American visitors who are above 35 years old tend to have a lower art museum attendance rate compared to the American visitors who are between 18-35 years old? Use α = 0.05.
β2 = 0 β2 < 0
-1.7886
lower one tailed
-1.7109
Decision rule Reject H0 in favor of Ha if the t-value < the lower CV.
Reject H0 in favor of Ha at α = 0.01.
There is significant evidence that American visitors who are above 35 years old tend to have a lower art museum attendance rate compared to the American visitors who are between 18-35 years old (α = 0.05).

Sheet4

Copy values from the regression output table:

Coefficients
SE

Intercept
25.1222222222
0.7994725628
23.4721919499
26.7722524946
Under 18
3.5222222222
1.130624941
1.1887270328
5.8557174117
Above 35
-2.0222222222
1.130624941
-4.3557174117
0.3112729672
Question:

Sample size
27

b (β estimate)
3.5222

SE
1.1306

DF
24

a
0.05

Upper CV

(from the CV calculator)

Lower CV

(from the CV calculator)

LB of the CI
1.189

UB of the CI
5.856

LB of 95% CI UB of 95% CI
Show how to calculate a 95% confidence interval for the β1 coefficient. How do you interpret the interval estimate in the context of the problem here?
Output Table: LB of the CI 1.189
UB of the CI 5.856
Verifying with Our Own Calculation
2.0639
-2.0639
CI Calculation: MOE 2.3335
Interpretation: The 95% CI for β1 = [1.189, 5.856]. It is estimated that the art museums attendance rate under the age of 18 is generally higher than that of those between the ages of 18 and 24 by an average 1.189 to 5.856 percentage points.

Sheet5

Statistic

Question:

Interpretation:

From the Regression Output Table:
R2 0.506525279
What does the R2 value tell us? Interpret the R2 value in the context of the problem here.
The model’s R2 value is around 0.5065. It means that age factor can account for about 50.65% of the variation in the data for art museum attendance rate by American visitors.

Sheet6

Copy values from the regression output table:

Coefficients
SE

Intercept
25.1222222222
0.7994725628

Under 18
3.5222222222
1.130624941

Above 35
-2.0222222222
1.130624941

Question:

from Excel’s Output Table:

25.12222
3.52222
-2.02222

Under 18
Above 35

Estimates

Under 18
1
0

Between 18-35
0
0

25.122

Above 35
0
1

Conclusion:

Provide average estimates for Americans art museum attendance rate in the age group of under 18 years old, between 18-35 years old, and above 35 years old.
Coefficient

Estimates
b0 b1 b2
Values for Predicting Variables: E(HSTART) = b0 + b1×SPRING + b2×SUMMER + b3×FALL
Age Group Formula used:
28.644 =$B$15 + SUMPRODUCT($C$15:$E$15,C18:E18)
=$B$15 + SUMPRODUCT($C$15:$E$15,C19:E19)
23.100 =$B$15 + SUMPRODUCT($C$15:$E$15,C20:E20)
The average estimates of Americans art museum attendance rate are 28.6% for the age under 18 years old , 25.1% for the age between 18-35 years old, and 23.1% for the age above 35 years old.

Expert paper writers are just a few clicks away

Place an order in 3 easy steps. Takes less than 5 mins.

Calculate the price of your order

You will get a personal manager and a discount.
We'll send you the first draft for approval by at
Total price:
$0.00