Analysis Of Statistical Variances Of Decision-Making Of Businesses Assignment Sample

Analysis Of Statistical Variances Of Decision-Making Of Businesses

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1.0 Question 1

1.1 Mean & Median Variances of Patient Waiting Times with&without wait-Tracking System

Mean	Median
17.2	13.5

Table 1: Mean & Median Variances of Patient Waiting Times With wait-Tracking System

(Source: Excel)

Mean	Median
29.1	13.5

Table 2: Mean & Median Variances of Patient Waiting Times Without wait-Tracking System

(Source: Excel)

1.2 Standard Deviation & Variances of Patients with & without tracking system

Variance	Standard Deviation
86.18	9.28

Table 3: Standard Deviation & Variances of Patients with Tracking System

(Source: Excel)

Variance	Standard Deviation
275.66	16.60

Table 4: Standard Deviation & Variances of Patients without Tracking System

(Source: Excel)

1.3 Analysis of the Box Plot for Patients Without Wait-tracking System

Min	12
Q1	16.75
Median	23.5
Q3	38.75
Max	67
Mean	29.1
IQR	22
Lower Limit	-16.25
Upper Limit	49.75

Table 5: Box Plot Calculation for Patients Without Wait-tracking System

(Source: Excel)

Figure 1: Box Plot for Patients Without Wait-tracking System

(Source: Excel)

1.4 Analysis of the Box Plot for Patients With Wait-tracking System

Min	9
Q1	11.75
Median	13.5
Q3	21.25
Max	0
Mean	17.2
IQR	9.5
Lower Limit	-2.5
Upper Limit	26

Table 6: Box Plot Calculation for Patients With Wait-tracking System

(Source: Excel)

Figure 2: Box Plot for Patients With Wait-tracking System

(Source: Excel)

1.5 Explanation of the shorter waiting times in offices with a wait-tracking System than Without a Wait-tracking System

According to the analysis of the mean and median variances of the addition of the wait tracking system & not addition with the wait tracking system, the patient waiting time is on an average lesser than the non-additional wait tracking system (Cleff, 2019). The average waiting time is observed at 17.2 with the wait tracking system & for the non-waiting tracking system, the period is observed at 29.31 which is less effective in patient management. With the wait tracking system, the reduction & the wastage of time of the patients is regulated & the standard variations are also regulated for an increase of the business & effective decision making.

2.0 Question 2

2.1 Summary & Explanation of the descriptive measures of the numerical output of two variances

In the analysis of the provided data collected from the perspective of the consumption of beer quantity per capita & the price of beer in Australia between the years 1975-2017 (Altig, 2022). The analysis of the descriptive measures regarding these two variances is shown in

Descriptive Measures of Data of the two variances of Beer Consumption from 1975-2017:

Beer Price(in $/per liter)	Beer Quantity (in liters)
Mean	10.35725698	Mean	133.86
Standard_Error	0.863544995	Standard_Error	4.736970414
Median	9.94625	Median	123.97
Mode	3.095947921	Mode	7.208069732
Standard Deviation	5.662643217	Standard Deviation	31.06239228
Sample Variance	32.0655282	Sample Variance	964.8722143
Kurtosis	-1.018076831	Kurtosis	-0.941286794
Skewness	0.285911047	Skewness	0.455317862
Range	19.13695	Range	105.65
Minimum	1.85055	Minimum	86.49
Maximum	20.9875	Maximum	192.14
Sum	445.36205	Sum	5755.98
Count	43	Count	43
Largest(1)	20.9875	Largest(1)	192.14
Smallest(1)	1.85055	Smallest(1)	86.49
Confidence Level(95.0%)	1.742704354	Confidence Level(95.0%)	9.55959332

Table 7: Chart of Descriptive Measures of Data of the two variances of Beer consumption from 1975-2017

(Source: Self-Created in MS Excel)

In the analysis of the descriptive measurement of the two variances of beer consumption quantity & the price of beer per liter, the primary key descriptive measures are discussed.

Through the descriptive measure of the Mean, the assessment of the average valuation of the data could be assessed (Ansari, 2019). In this case, the mean value of the price of beer is observed at around 10 Australian dollars per liter, throughout the time period & the average beer consumption quantity is observed at around 133.86 liters, throughout the time period. 

Through the variance of the Median, the average distribution of the valuation could be assessed (CEPAL, 2019). In this case, the average valuation of the price distribution of beer is observed at 9.94 Australian Dollars & the quantity distribution is observed at 123.97 liters of beer.

Through the Mode variance, the common & popular choices of the variances are being signified (Ciampi, 2021). In this case, the mode variance is observed at around 32.065 in the perspective of the pricing of beer & in the perspective of the quantity of the beer the valuation is observed at around 7.2. 

2.2 Comments on the descriptive measures of two variances

Through the analysis of the Descriptive measures, there are various statistical attributes have been observed, that have been describing the overall variances in beer consumption in Australia (Craven, 2020). Through the mean-variance of the pricing of beer, the average valuation is observed at around 10.35 Australian dollars & the average consumption is observed at 133.86 liters. As per the observation of the data, the highest price valuation was observed at 20.99 Australian dollars per liter in the recent year 2017 & the lowest valuation is observed in the year 1975, which is valued at 1.85 Australian Dollars per liter (Kim, 2020). Through this understanding of the variances, we could get an insight into the population factor of the country. In 1975, the volume of the population in Australia was way lesser than in the modern days. As the material cost & production cost of making beer was also way lesser according to the customer demand. As the consumption value was much higher than the recent years, which is around 30 liters higher than in 2017. As the demand of consumption of beer is gotten higher in recent years, the price valuation has also risen, which has differed by around 19 Australian Dollars. The significant increase in price has observed a reduction in consumption. The sum of the price variance of beer is observed at 445 dollars per liter& the quantity of consumption is valued at around 5755 liters between the years of 1975-2017 among the population of Australia (Kodali, 2020). Through the sample variance, the expected valuation of the variables could be assessed. In this case, the sample variance of the beer price is observed as 32 dollars, which is projected for the future estimation of the price range of beer & for the estimation of the quantity of beer consumption valued at 964 liters. This analysis is being done on 43 variances of the provided data.

2.3 Testing of the Hypothesis

T-test Regarding Hypothesis:

Beer Price(in $/per litre)	Beer Quantity (in liters)
Mean	14.43879167	110.1025
Variance	15.02539547	141.9977848
"Observations"	24	24
Pooled Variance	78.51159012
Hypothesized Mean Difference	0
df	46
t Stat	-37.39994369
P(T<=t) one-tail	2.19815E-36
t Critical one-tail	1.678660414
P(T<=t) two-tail	4.39631E-36
t Critical two-tail	2.012895599

Table 8: Chart of Descriptive Measures of Data of the two variances of Beer consumption from 1994-2017

(Source: Self-Created in MS Excel)

In the analysis of the variances the test hypothesis was created, which is variated according to the mean valuation of the population that has the beer consumption of 135 liters per year. It is observed from the year 1994 (Kurniasih, 2019). The average price of the bear is observed at 15 dollars per liter. In this time period, the increase of demand for beer consumption had increased to 110 liters of the average consumption of beer per year. The "Observations" of valuations are observed from the comparison of pooled variances. The Pooled variance is observed at 78.22 of the price valuation of consumption of beer.

2.4 Explanation of Researcher Claims

Through the differentiating analysis of the variances of the consumption & pricing of the beer with the comparison of population per capita of 135liters/year, it is agreeable that the population per capita is higher or greater than the 135 liters/year, as the growing number of population in the recent years has observed an increased demand for the consumption (Lu,2021). As the demand is increasing by the day pass the increase of the pricing per liter could be observed through the understanding of the sample variance, the predictive price is estimated at around 32 dollars per liter& the increased quantity of consumption has slightly increased to 962 liters per year.

2.5 Analysis of Beer Consumption in Australia

Through the detailed understanding of the research hypothesis, the mean valuation of the population per capita is significant in the assessment of the prices of beer & the overall consumption is assessed (Ridgway,2021 ). According to the data set, the increase in the population has grown the demand for consumption & also increased the material cost of beer production. In recent days, the increase in the price is also observed as the increase in the population of Australia is in progress. The further increase in the price range will be increasing & the estimation of the revenue generation will also increase. Through the increase in the population, the increase in consumption is natural.

3.0 Question 3

3.1 Discussion of Numerical Descriptive& Linear Relationship of Variances

"Regression Statistics"
Multiple_R	0.8095129
R_Square	0.6553111
Adjusted R_Square	0.5863733
Standard_Error	0.8366684
"Observations"	7

Table 9: "Regression Statistics" "Summary (Output)” between weekly gross revenue and television advertising

(Source: Excel)

df	SS	MS	F	Significance F
Regression	1	6.654215847	6.6542158	9.5058329	0.027371402
Residual	5	3.500069867	0.700014
Total	6	10.15428571

Table 10: Regression Analysis Output: ANOVA between weekly gross revenue and television advertising

(Source: Excel)

Coefficients	Standard_Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2.290193069	0.73287148	3.124958649	0.026105585	0.406286955	4.174099183	0.406286955	4.174099183
101.3	0.015027539	0.004874081	3.083153075	0.027371402	0.002498314	0.027556765	0.002498314	0.027556765

Table 11: Regression Analysis Output: Coefficient between weekly gross revenue and television advertising

(Source: Excel)

Observation	Predicted 5	Residuals
1	3.070122356	-0.070122356
2	3.414253005	0.585746995
3	4.186668522	0.113331478
4	4.360987978	-0.760987978
5	3.813985549	-0.313985549
6	5.863741902	-0.863741902
7	5.590240688	1.309759312

Table 12: Regression Analysis Output: Residual between weekly gross revenue and television advertising

(Source: Excel)

"Regression Statistics"
Multiple_R	0.910114013
R_Square	0.828307517
Adjusted R_Square	0.793969021
Standard_Error	1.057848074
"Observations"	7

Table 13: "Regression Statistics" "Summary (Output)” between weekly gross revenue and newspaper advertising

(Source: Excel)

df	SS	MS	F	Significance F
Regression	1	26.99335869	26.99335869	24.12183409	0.004430411
Residual	5	5.595212741	1.119042548
Total	6	32.58857143

Table 14: Regression Analysis Output: ANOVA between weekly gross revenue and newspaper advertising

(Source: Excel)

Coefficients	Standard_Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	0.080225968	0.926611672	0.086579924	0.934365734	-2.301705164	2.4621571	-2.301705164	2.4621571
101.3	0.030266896	0.006162582	4.911398384	0.004430411	0.014425475	0.046108318	0.014425475	0.046108318

Table 15: Regression Analysis Output: Coefficient between weekly gross revenue and newspaper advertising

(Source: Excel)

Observation	Predicted 1.5	Residuals
1	1.651077896	1.348922104
2	2.344189826	-0.844189826
3	3.899908306	0.400091694
4	4.251004305	-0.251004305
5	3.149289273	-0.849289273
6	7.277693955	1.122306045
7	6.726836439	-0.926836439

Table 16: Regression Analysis Output: Residual between weekly gross revenue and newspaper advertising

(Source: Excel)

In the analysis of the variances of the descriptive measures, the Multiple Regression is observed 0.9011 in the 7 "Observations" (Ruggeri, 2020). The predictive 1.5 of the "Observations" is observed to increase in the variations. In the sixth observation, the valuation is increased to 7.27 in the regression analysis of the weekly generation of revenue & the advertisement of the newspaper (Su,2022). As per the "Observations" of the residuals of the regression of weekly gross profit & television advertisement, a stable prediction is observed, as the variances do not have much fluctuation. This is signifying a stable correlation between the two mediums. The advertisement in newspapers is crucially variating in the correlation of the generation of gross revenue.

3.2 Linear regression between the variances

"Regression Statistics"
Multiple_R	0.7451076
R_Square	0.5551854
Adjusted R_Square	0.4810496
Standard_Error	0.8843301
"Observations"	8

Table 17: Simple Linear "Regression Statistics" "Summary (Output)” between "weekly gross revenue and television advertising expenditure"

(Source: Excel)

df	SS	MS	F	Significance F
Regression	1	5.856511595	5.8565116	7.4887648	0.033889855
Residual	6	4.692238405	0.7820397
Total	7	10.54875

Table 18: Simple Regression Analysis Output: ANOVA between "weekly gross revenue and television advertising expenditure"

(Source: Excel)

Coefficients	Standard_Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2.592321833	0.734954086	3.527188816	0.012409919	0.793953969	4.390689696	0.793953969	4.390689696
X Variable 1	0.013857466	0.005063825	2.736560752	0.033889855	0.001466731	0.026248201	0.001466731	0.026248201

Table 19: Simple Regression Analysis Output: Coefficient between "weekly gross revenue and television advertising expenditure"

(Source: Excel)

3.3 Comments on the estimated model

Through the instigation of the simple linear regression, the concerns of two variances is coordinated according to the predictions of the dependent variables (Truong,2020). Through the predictions of the dependent variables, the functioning of the independent variable is predicted. In this case, the dependent variable is the television advertisement expenditure. The output of the Fitting of goodness in the simple linear regression model is differentiated into Intercept & X variables (Zaragoza, 2021). For the intercept, the upper valuation is estimated at 4.39 & the lower estimation is valued at 0.7939. The differentiation is observed in 3 points, which is a huge variation difference in the coefficients. The coefficients are observed in the valuation of around 2.59 for intercept & 0.01 for X variable 1. Through the simple regression analysis, two factors are being estimated & evaluated in relation to the regulation of the expenditure.

3.4 Evaluation of estimated model

In the valuation of the simple linear regression the evaluation of the fit of goodness is possible through the effective creation of the relations between the gross revenue generations with the television advertisement & newspaper advertisement. The gaining popularity of television is constantly improving as it is much more attractive in the effective promotions of any products &services (Zawada,2020). As the number of readers of newspapers is gradually reducing due to the increased advancement of technologies. Through the equilibrium of these factors of advertisement, the effective revenue generation for all businesses. Through this, the evaluation of the simple linear regression model in the analysis of the relation of gross revenue & advertisement expenditure would be regulated for business development.

3.5 Estimation of Multiple Regression model

"Regression Statistics"
Multiple_R	0.96552034
R_Square	0.93222953
Adjusted.R_Square	0.90512134
Standard_Error	20.3315702
"Observations"	8

Table 20: Multiple Linear "Regression Statistics" "Summary (Output)” between "weekly gross revenue and television and newspaper advertising expenditure"

(Source: Excel)

df	SS	MS	F	Significance F
Regression	2	28431.13627	14215.5681	34.389224	0.001195642
Residual	5	2066.863733	413.372747
Total	7	30498

Table 21: Multiple Regression Analysis Output: ANOVA between "weekly gross revenue and television and newspaper advertising expenditure"

(Source: Excel)

Coefficients	Standard_Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-42.56959361	28.5471741	-1.491201667	0.196106771	-115.9524408	30.81325359	-115.9524408	30.81325359
Television Advertising ($100s)	22.40223856	7.099331722	3.155541879	0.025221229	4.152825395	40.65165173	4.152825395	40.65165173
Newspaper Advertising ($100s)	19.49862752	3.696946525	5.274251978	0.003260339	9.995323936	29.0019311	9.995323936	29.0019311

Table 22: Multiple Regression Analysis Output: Coefficient between "weekly gross revenue and television and newspaper advertising expenditure"

(Source: Excel)

3.6 Analysis of the regression coefficients

Through the analysis of the multilinear regression between the independent variable of weekly gross revenue with the independent variables of television advertisement & newspaper advertisement, the variations of the coefficient variances is prevalent. For the comparison of the television advertisement the valuation of the coefficient is observed at 22.402 & the variance of newspaper advertisement is observed at 19.498 which is signifying the popularity of the television advertisement for the generation of gross revenue (Couture, 2019). On the upper linear limit, television advertisement is valued at 40.651 & the lower estimation is valued at 4.15, which is higher than the newspaper advertisements. The higher estimation is 29.001 & the lowest estimation is observed at 9.99. In the equilibrium of these dependent variables, effective relations could be established for the effective evaluation of the business.

3.7 Testing of Overall Validity of the estimated regression model at a 5% significance level

In the testing of the outputs of the multiple linear regression, the general significance level is observed at 0.05 %. The estimation of the significance Level at 5% is a risk factor for the business evaluation. The lower levels of significance are the probability for the differentiated probability of the variances through the acceptance of the indication for stronger evidence of the hypothesis & the sampling process. There is various statistical hypothesis that is observed. From the eight "Observations", the intercept & the comparison of the lower-value & the upper-value productivity should be regulated in the business evaluation. The increase in significance level to 5% is a grave risk factor as it is signifying the overestimation of the valuation of the regression model.

3.8 Test of the linear relationship of independent variables at a 5% significance level

As the relations of the linear relationship of the Independent variables, the increase of significance level to 5% is also critical for the independent variable, which is consisted of the dependent variable. The regulator significance level is observed as 0.5 %. The risk level is way higher in the evaluation of the business. Through the regression analysis the evidence of the differentiated manner.

3.9 Conclusion of the change in significance level to 1%

In the regulation of the significance level from 5% to 1%, the regulation of the overestimation & the risk factors of the linear relationship could be variated in the better understanding of the variances. Through the equilibrium between the variances by the reduction of the significance level, the business evaluation could be observed for profit maximization.

3.10 Comparison of the Regression Models

Analysis of regression is basically used in investment & finances. In the simple linear regression, the establishment of the relation between two variables are in the depiction with the changes of one variable. Through the y incept the representation of the linear regression is evaluated in the changes than the increase of the greater flexibility of the non-linear regression.

In comparison with Multiple Regression, the attempts to explanation of the dependent variables & independent variables. There are variation changes that could be observed in the multiple regression model.

3.11 Research report

In the overall analysis of the regression analysis of the variations of the variables, the independent variable is the weekly gross revenue. The variations are dependent upon the gaining popularity of the advertisement.

In the analysis of the variables, the analysis of the multilinear regression between the independent variable of weekly gross revenue with the independent variables of television advertisement & newspaper advertisement, the variations of the coefficient variances is prevalent. For the comparison of the television advertisement the valuation of the coefficient is observed at 22.402 & the variance of newspaper advertisement is observed at 19.498 which is signifying the popularity of the television advertisement for the generation of gross revenue. The instigation of the simple linear regression, the concerns of two variances are coordinated according to the predictions of the dependent variables (Pearson.com, 2021). Through the predictions of the dependent variables, the functioning of the independent variable is predicted. In this case, the dependent variable is the television advertisement expenditure. The output of the Fitting of goodness in the simple linear regression model is differentiated into Intercept & X variables. For the intercept, the upper valuation is estimated at 4.39 & the lower estimation is valued at 0.7939. The differentiation is observed in 3 points, which is a huge variation difference in the coefficients. As per the "Observations" of the residuals of the regression of weekly gross profit & television advertisement, a stable prediction is observed, as the variances do not have much fluctuation. This is signifying a stable correlation between the two mediums.

References

Books

• Cleff, (2019) Applied Statistics and Multivariate Data Analysis for Business and Economics available at link.springer.com/book/10.1007/978-3-030-17767-6 [Accessed on 16.5.2023]

Journals

• Altig, D., Barrero, J.M., Bloom, N., Davis, S.J., Meyer, B. and Parker, N., 2022. Surveying business uncertainty. Journal of Econometrics, 231(1), pp.282-303.
• Ansari, S., Ansari, G., Ghori, M.U. and Kazi, A.G., 2019. Impact of brand awareness and social media content marketing on consumer purchase decision. Journal of Public Value and Administrative Insight, 2(2), pp.5-10.
• CEPAL, N., 2019. Proposal for a generic law on official statistics for Latin America.
• Ciampi, F., Demi, S., Magrini, A., Marzi, G. and Papa, A., 2021. Exploring the impact of big data analytics capabilities on business model innovation: The mediating role of entrepreneurial orientation. Journal of Business Research, 123, pp.1-13.
• Craven, M., Liu, L., Mysore, M. and Wilson, M., 2020. COVID-19: Implications for business. McKinsey & Company, 8.
• Kim, J.H., Choo, W. and Song, H.O., 2020, November. Puzzle mix: Exploiting saliency and local statistics for optimal mixup. In International Conference on Machine Learning (pp. 5275-5285). PMLR.
• Kodali, L., Sengupta, S., House, L. and Woodall, W.H., 2020. The value of summary statistics for anomaly detection in temporally evolving networks: A performance evaluation study. Applied Stochastic Models in Business and Industry, 36(6), pp.980-1013.
• Kurniasih, N., Ahmar, A.S. and Kurniawati, N., 2019. Utilization of Statistics for Provision of Business Information: Implementation of α-Sutte Indicator on Provision of Stock Movement Prediction Information. Library Philosophy and Practice, pp.NA-NA.
• Lu, J., Cairns, L. and Smith, L., 2021. Data science in the business environment: customer analytics case studies in SMEs. Journal of Modelling in Management, 16(2), pp.689-713.
• Ridgway, J., Statistics for empowerment and social engagement: Teaching Civic Statistics to develop informed citizens.(Chief Editor: Jim Ridgway).
• Ruggeri, K., Alí, S., Berge, M.L., Bertoldo, G., Bjørndal, L.D., Cortijos-Bernabeu, A., Davison, C., Demi?, E., Esteban-Serna, C., Friedemann, M. and Gibson, S.P., 2020. Replicating patterns of prospect theory for decision under risk. Nature human behaviour, 4(6), pp.622-633.
• Su, W., Zhang, L., Zhang, C., Zeng, S. and Liu, W., 2022. A Heterogeneous Information-Based Multi-Attribute Decision Making Framework for Teaching Model Evaluation in Economic Statistics. Systems, 10(4), p.86.
• Truong, P.H., Hang, N.T.T. and Tan, B.M., Analysis on the Application of Mathematical Statistics in the Field of Modern Economy and Management.
• Zaragoza, M.P.P. and Cruz, M.S., 2021. The Territorial Organization of Public Tourism Statistics in Spain: A Problem of Date Generation and Use in Geomarketing. In Marketing and Smart Technologies: Proceedings of ICMarkTech 2020 (pp. 225-237). Singapore: Springer Singapore.
• Zawada, P., Okrasa, W. and Warchalowski, J., 2020. Flow management system for maximising business revenue and profitability. Statistics in Transition new series, 21(5), pp.193-206.

Article

• Couture, (2019) A Fuzzy Logic Based Machine Learning Tool for Supporting Big Data Business Analytics in Complex Artificial Intelligence Environments available at ieeexplore.ieee.org/abstract/document/8858791 [Accessed on 16.5.2023]

Website

• Pearson.com, (2021) Statistics for Business Decision Making & Analysis available at www.pearson.com/en-us/subject-catalog/p/statistics-for-business-decision-making-and-analysis/P200000006351/9780137399727 [Accessed on 16.5.2023]