group report group presentation end of term

Is there any statistically significant difference between the 2 groups of gender in terms of Income?. Null Hypothesis HO: There is no statistically significant difference in income betwe

UNIVERSITY OF ECONOMICS HO CHI MINH CITY

BUSINESS SCHOOL

FACULTY OF INTERNATIONAL BUSINESS - MARKETING

UEH

UNIVERSITY

GROUP REPORT

GROUP PRESENTATION — END OF TERM

Lecturer: PhD Nguyen Van Dung

Subject: Business Analysis

Course ID: 24D1BUS50320001

Date: Wednesday morning

Ho Chi Minh City, May 12, 2024

Table of Contents

2 Make a frequency table about Educational level Requirements: (1) number of observations for

each level and (11) specific percentage for each level Which level of education accounts for the

highest percentage? Which level of education accounts for the lowest percentage? 1

3 Draw a pie chart showing the percentage of observations by Gender (male, female) Show the

specific percentages on the graph In the sample, males or females accounted for a higher

JOSE 0) 010) 18 (0) cc cc cc cor 2

4, Compare the mean of Income of the 2 groups of gender Is there any statistically significant

difference between the 2 sroups of gender 1n terms of Ïneorn€? ‹ c1 1121111112111 2

5 Compare the mean of Income among different educational levels Is there any statistically

significant difference among educational levels in terms oŸ Income? - cá c2 s22 4

6 Check whether there is multicollinearity among the variables: Age, Gender, Education,

„/bitrJRorin 88.900 5852.<2v01.- yPnn 6 6

7, Use multiple linear regression to analyze the impact of the variables Age, Gender, Education,

Martital status, Doing exercIses on the variable Ïncorme i c1 101121211 1 1110111111 7

8 Create an interaction variable between Age and Doing exercises Analyze the moderating

effect of Doing exercises on the relationship between Age and Ineorme? - ác s2 10

GROUP 4

Name Student ID Task completion

Nguyễn Thị Thanh Ngân 31221024484 100%

Đặng Võ Như Quỳnh 31221026177 100%

Lê Cao Nhật Anh 31221020690 100%

Đặng Thị Hà Nhu 31221026107 100%

Phạm Phan Hà My 31221025378 100%

Bùi Băng Nhi 31221026104 100%

Bùi Như Quỳnh 31221026123 100%

2 Make a frequency table about Educational level Requirements: (i) number of

observations for each level and (ii) specific percentage for each level Which level of

education accounts for the highest percentage? Which level of education accounts for the

lowest percentage?

Statistics

Education:

N Valid 100

Missing

Education:

Frequency Percent Valid Percent Cumulative Percent

Valid THPT 21 21.0 21.0 21.0

Dai hoc 70 70.0 70.0 91.0

Thạc sĩ 7.0 7.0 98.0

Tiến sĩ 2.0 2.0 100.0

Total 100 100.0 100.0

The table describes the number of observations for each level of education and their proportion

in the total extent It can be drawn from the table that “College Student” accounts for the highest

number with 70 observations, accounting for 70% of the sample

On the other hand, “Ph.D Master” is the smallest group with only 2 observations, which only

capture 2 % of the sample

3 Draw a pie chart showing the percentage of observations by Gender (male, female)

Show the specific percentages on the graph In the sample, males or females accounted for

a higher proportion?

Pie Chart Count of Gender:

Gender:

#Femals

Bae

The Pie chart illustrates that within the surveyed sample, the gender distribution shows a fairly

balanced split between males and females, with 48% for males and 52% for females This

suggests a relatively even distribution of genders within the dataset

4 Compare the mean of Income of the 2 groups of gender Is there any statistically

significant difference between the 2 groups of gender in terms of Income?

A Descriptive Statistics:

- Male Group:

@ Mean Income: 12.92

e Standard Deviation: 8.470

- Female Group:

@ Mean Income: 11.25

e Standard Deviation: 9.800

Group Statistics

| Gchder: N Mean Std Deviation Std Error Mean

Income: Female 52 11.25 9.800 1.359

Male 48 12.92 8.470 1.223

B Hypothesis Stating:

1 Null Hypothesis (HO): There is no statistically significant difference in income between male

and female groups

If P-value > a, the null hypothesis (HO) is not rejected, suggesting no statistically significant

difference in income

2 Alternative Hypothesis (H1): There is a statistically significant difference in income between

the male and female groups

If P-value < a, the null hypothesis is rejected, indicating a statistically significant difference in

income between the two groups

Give the significant level (a) of 0,05

€, Levene”s test

According to the statistical table described above, Sig of the test F = 0.865 > 0.05 => fail to

reject the HO: there is no difference in the variance of the 2 populations => use the results in the

lie Equal variances assumed

Independent Samples Test

Levene's Test

for

Equality of

Variancettest for Equality of Means

95% Confidence

Interval of the

Sig (Mean Std Error Difference

Sig df tailed) Difference Differenkewer Upper

Income: Equal 029 865 -.906 98 367 -1.667 1.839 -5.315 1.982

variances

assumed

Equal -.912 97.592 364 -1.667 1.828 -5.294 1.961

variances

not

assumed

D Results

Based on the independent sample test results, with a p-value or significance level of 0.367 > 0.05

sit is concluded that the null hypothesis is not rejected This suggests that there is no statistically

significant difference between the mean incomes of males and females

In other words, it implies that there is no significant evidence in income between the two

genders

5 Compare the mean of Income among different educational levels Is there any

Statistically significant difference among educational levels in terms of Income?

Descriptives

Income:

95% Confidence Interval

for Mean

N Mean — Std Deviaticiitd Errorf_ower BoundJpper BoundVinimum Maximum

THPT 21 910 8414 1.836 5.27 12.93 30

Đại học 70 10.56 6.606 790 8.98 12.13 30

Thạc sĩ 27.14 4298 1625 23.17 31.12 20 32

Tiến sĩ 42.50 3.536 2.500 10.73 74.27 40 45

Total 100 12.05 9.178 918 10.23 13.87 45

According to the statistical table described above, in the Mean column the average value

of Income of the High school education is 9.10, University is 10.56, MA is 27.14 and

PhD 42.50 Which values from 9.10 to 42.50 elements representing each income level

gradually increases

— So it is clear that income will be proportional to education level The high school education

level is average lowest income among the three qualifications above; and vice versa, PhD level

of education has the highest average income

Test of Homogeneity of Variances

Levene Statistic dfl df2 Sig

Income: Based on Mean 1.467 96 228

Based on Median 852 96 469

Based on Median and wifh2 72.970 470

adjusted df

Based on trimmed mean 1.155 96 331

- According to table “Test of Homogeneity of Variances” above, Sig of the Levene

statistic of the Income average per month is 0.228 > 0.05 So at 95% confidence that the

hypothesis HO “The variance is equal” are accepted, and reject hypothesis H1: “The

variance is different”

— Hence, the result of ANOVA analysis can be used

ANOVA

Income:

Sum of Squares df Mean Square Sig

Between Groups 3788.312 1262.771 26.641 000

Within Groups 4550.438 96 47.400

Total 8338.750 99

- According to the ANOVA table above, it results of ANOVA analysis with a significance

level of 0.000 < 0.05, thus the observational data are qualified to confirm that there is a

difference in average monthly income between groups with different levels of education

— There is a statistically significant difference between educational levels and income

Robust Tests of Equality of Means

Income:

Statistic* dfl df2 Sig

Welch 57.206 4.843 000

a Asymptotically F distributed

6 Check whether there is multicollinearity among the variables: Age, Gender, Education,

Marital status, Doing exercises?

Correlations

Age: Gender: Education: Marital status:Doing exercises:

Age: Pearson Correlation 083 220° 618” 136

Sig, (2-tailed) 412-028 000 177

N 100 100 100 100 100

Gender: Pearson Correlation083 -.074 053 088

Sig (2-tailed) 412 462 604 386

N 100 100 100 100 100

Education: Pearson Correlation 220° -.074 170 199°

Sig (2-tailed) 028 462 091 048

N 100 100 100 100 100

Marital status: Pearson Correlaton6l8” .053 170 140

Sig (2-tailed) 000 604 091 164

N 100 100 100 100 100

Doing exercises:Pearson Correlation 136 088 199° 140

Sig(2tailed)ọ 177 386 .048 164

N 100 100 100 100 100

* Correlation is significant at the 0.05 level (2-tailed)

** Correlation is significant at the 0.01 level (2-tailed)

According to Correlations tables, we can see that:

- The correlations of “Age-Gender” is 0.083, “Age-Education” is 0.220, “Age-Marital

status” is 0.618, “Age-Doing exercises” is 0.136 4 + 0.7 So there is no multicollinearity

between these pairs of variables

- Similarly, the correlation between two variables: “Gender - Education” is -0.074,

“Gender - Marital status” is 0.053, “Gender - Doing exercises” is 0.088, “Education -

Marital status” is 0.170, “Education - Doing exercises” is 0.199, “Marital status - Doing

exercises’ is 0.140 All indexes are equal less than + 0.7, so it can be concluded that each

individual pair of variables does not have multicollinearity

— It means that there is no problem of multicollinearity

7 Use multiple linear regression to analyze the impact of the variables Age, Gender,

Education, Marital status, Doing exercises on the variable Income?

A Linear Regression Model

By utilizing a multiple linear regression model, we can analyze the impact of the five

independent variables Age, Gender, Education, Marital status, and Doing exercises on the

dependent variable Income The model equation is as follows:

Y=B0+BIXI+B2X2+B3X3+B4X4+BSX5+e

Where:

e Y is the dependent variable Income

e© XI, X2, X3, X4, Xã are the mdependent variables Age, Gender, Education, Marital

status, Doing exercises respectively

® 0 represents the intercept

e £1, 62, £3, B4, B5 are respective coefficients for the independent variables

e erepresents the error term

B R square & Interpretation:

Model Summary

Model R Square Adjusted R Square Std Error of the Estimate

834° 695 679 5.201

a Predictors: (Constant), Gender:, Marital status:, Doing exercises:, Education:, Age:

The value of R2 indicates that 70% of the variation in Income is explained by five independent

variables

C Hypothesis stating and testing:

H0: B1 = B2 = B3 = B4 = B5 If P > a, the null hypothesis (HO) is not rejected, suggesting no

statistically significant relationship H1: At least one By #0

If P <a, the null hypothesis (HO) is rejected, suggesting a statistically significant relationship

exists

ANOVA?’

Model Sum of Squares df Mean Square Sig

Regression 5796.032 1159.206 42.854 000°

Residual 2542.718 94 27.050

Total 8338.750 99

a Dependent Variable: Income:

b Predictors: (Constant), Gender:, Marital status:, Doing exercises:, Education:, Age:

Test Statistic: F-stat = 42,854, which yields a P-value of 0,000 < oa Therefore, the null

hypothesis is rejected and there is a significant relationship between the dependent variable and

at least one independent variable

D Linear regression result

Coefficients*

Standardized

Unstandardized Coefficients Coefficients

Model Std Error Beta Sig

(Constant) -15.610 2.408 -6.482 000

Doing exercises: 915 1.088 049 841 402

Age: 522 084 459 6.240 000

Education: 6.004 921 389 6.516 000

Marital status: 4.525 1.361 242 3.325 001

Gender: 1.188 1.054 065 1.127 262

a Dependent Variable: Income:

Looking at the p-values for the independent variables in the last section, we see that two of the

five independent variables have P-values that exceed the Significant level and therefore, are no

statistically significant

By removing the variables with the highest P-value (Doing exercises) and re-analyze the model,

we could create an improved regression model:

Coefficients*

Standardized

Unstandardized Coefficients Coefficients

Model Std Error Beta Sig

(Constant) -15.470 2.399 -6.450 000

Age: 524 084 461 6.278 000

Education: 6.144 905 398 6.790 000

Marital status: 4.600 1.356 246 3,392 001

Gender: 1.273 1.048 070 1.215 227

a Dependent Variable: Income:

Gender P-value remains higher than the Significant level, indicating that the variable has no

statistical significance in the model and should be removed The regression model follows the

coefficient tables as bellow:

Coefficients*

Standardized

Unstandardized Coefficients Coefficients

Model Std Error Beta Sig

(Constant) -14.866 2.352 -6.320 000

Age: 532 083 468 6.377 000

Marital status: 4.609 1.359 246 3.391 001

Education: 6.039 903 391 6.688 000

a Dependent Variable: Income:

Y= -14.866 + 0,532X1 + 4,609X2 + 6,039X3 + €

E Interpretation of result

With the exclusion of X4 and X5 from the model, the interpretation of the result is as follows:

e The coefficient of Age is statistically significant and positive This indicates that age has

a positive influence on income If age increases by 1 year, income increases by 0,532

million VND, keeping all other independent variables constant

e The coefficient of Marital status is statistically significant and positive This indicates

that level of education has a positive influence on income If education increases by 1

level, income increases by 4,609 million VND, keeping all other independent variables

constant

e The coefficient of Education is statistically significant and positive This indicates that

marital status has a positive influence on income If the observation is married, income

increases by 6,039million VND, keeping all other independent variables constant

8 Create an interaction variable between Age and Doing exercises Analyze the moderating

effect of Doing exercises on the relationship between Age and Income?

ANOVA?

Model Sum of Squares df Mean Square Sig

Regression 4482.916 1494.305 37.204 000°

Residual 3855.834 96 40.165

Total 8338.750 99

a Dependent Variable: Income:

b Predictors: (Constant), Interaction, Age:, Doing exercises:

— The ANOVA table illustrated that this model is reliable (Sig < 0.05)

Coefficients*

Standardized

Unstandardized Coefficients Coefficients

Model Std Error Beta Sig

(Constant) -2.993 3.768 -.794 429

Age: 517 149 454 3.459 001

Doing exercises: -6.773 4.600 -.366 -1.472 144

Interaction 371 177 599 2.101 038

a Dependent Variable: Income: