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Linear Analysis

Executive Summary

The purpose of the paper is to present an analysis day’s cash spending by travelling parties at a festival. The data included the following variables:

  1. spending one day’s cash expenditure at festival,
  2. number of people – number of individual in the party,
  3. days- planned – number of days in attendance;
  4. reason – what is the primary attraction to the festival which includes the following:
  • Shows & Music: attending because of the quality or type of music and artists.
  • Cost: attending because it is a relatively inexpensive entertainment or vacation.
  • Rides & Attractions: attending for the carnival-style rides and attractions.
  • Convenience: attending because it is close by and easy to get to.
  • Wine & Food: attending for the specialty wine and food exhibits, vendors, and tastings.

The analysis paper starts with an introduction of the data to be analysed and formulate hypothesis of the case. Later, it explains the data collection procedures that were used to collect the data in the festival. The finding from the analysis is explained in the proceeding section and decision of the finding in detail. Lastly, paper finishes with the conclusion of the case study.

Linear Analysis Introduction

The purpose of this analysis is to identify significant predictors of single day cash spending by travelling parties at a festival. The interpretation includes fortitude of significant determinants together with an explanation of their empirical relationship to single day spending. Based on correlation and regression analysis and testing, the following data-based hypothesis/expectations will be tested: the number of people that affect spending during the festivals. The analysis demands to check the correlation between the number of people and the spending patterns of visitors of the festivals from the data. The hypothesis is that there is a positive correlation between the number of people and spending during the festivals.
The number of days also influences the spending during the festivals. It expected that visitors who plan to spend more time at the festival would carry more money with them, therefore, spend more during the festival. We can assume that people who wish to spend more time in the festival are wealthier, because they have more time for leisure activities. From the data we can state the hypothesis that there is a positive correlation between the number of days and spending during the festivals.
Furthermore, we can also formulate the last hypothesis that relates with reasons for going to the festival and spending. There were five reasons why people visit the festival, such as:

  • Shows & Music: attending because of the quality or type of music and artists.
  • Cost: attending because it is a relatively inexpensive entertainment or vacation.
  • Rides & Attractions: attending for the carnival-style rides and attractions.
  • Convenience: attending because it is close by and easy to get to.
  • Wine & Food: attending for the specialty wine and food exhibits, vendors, and tastings.

In order to perform the following correlation, we are going to perform data coding as shown on the table

Table 1: Data Coding
RESPONDENT Survey number — data coding key
SPENDING One day’s cash expenditure at festival
#PEOPLE Number of individuals in the party
DAYS Planned number of days in attendance
REASON What is the primary attraction of the festival?
  • Show s& Music: attending because of the quality or type of music and artists. Coded as 0
  • Cost: attending because it is a relatively inexpensive entertainment or vacation. Coded as 1
  • Rides & Attractions: attending for the carnival-style rides and attractions. Coded as 2
  • Convenience: attending because it is close by and easy to get to. Coded as 3
  • Wine & Food: attending for the specialty wine and food exhibits, vendors, and tastings. Coded as 4

From the retrieved data we can state that there is a correlation, since the type of leisure activities have different cost, then a correlation must exist between the reason for going to the festival and the spending.
There is a positive correlation between the reason for going and spending during the festivals.

Methodology

To identify significant predictors of single day cash spending by travelling parties at a festival, data was collected at the festival from 154 visitors. Questionnaires were used as the data collection instruments and the data generated was fed into an excel sheet. The data information was retrieved regarding the (i) spending one day’s cash expenditure at festival, (ii) number of people – number of individuals in the party, (iii) days-planned number of days in attendance, (iv) reason- what is the primary attraction to the festival. Summary of the information about 154 visitors during the festivals is presented in the table below:

Table 2. Summary Statistics for the Festival
Correlation SPENDING (USD) DAYS PEOPLES Shows & Music Cost Convenience Wine & Food Rides & Attractions
SPENDING (USD) 1.00
DAYS 0.39 1.00
PEOPLES 0.48 0.31 1.00
Shows & Music 0.08 0.31 -0.12 1.00
Cost -0.19 -0.27 -0.15 -0.19 1.00
Convenience -0.07 -0.08 0.18 -0.30 -0.25 1.00
Wine & Food 0.09 0.07 0.04 -0.21 -0.17 -0.28 1.00
Rides & Attractions 0.08 -0.04 -0.01 -0.26 -0.22 -0.34 -0.24 1.00

The descriptive correlation showed positive strong correlation among some of the variables: days and people. However, there was a negative correlation or little correlation between the reason for going and spending. For instance, Shows and Music 0.08, Cost – 0.19, Convenience, -0.07, Wine and Food 0.09 and Rides and Attraction 0.008

Findings

Regression analysis was used to examine the collective relationship between the independent variables and spending level. All the variables were fed into a linear regression and the out recorded in Table 3. The overall fit model showed a R2 = 0.32 Adjusted R2 = 0.3 showing it was not good fit. This implied that there might be errors during the data collection procedures.

Table 3. Regression Statistics for the Festival
Multiple R 0.57
R Square 0.32
Adjusted R Square 0.30
Standard Error 39.67
Observations 154.00

Table 4 showed a Significance F = O which represent the P value = 0 showing that the event is impossible in the context of the finding.

Table 4. ANOVA
ANOVA df SS MS F Significance F
Regression 6.0 110537.6 18422.9 11.7 0.0
Residual 147.0 231358.6 1573.9
Total 153.0 341896.2

Table 5 showed both positive and negative coefficients with regard to spending. This indicated the nature of direction of the effect. For instance spending is expected to increase (if the coefficient is positive) or decrease (if the coefficient is negative). However, in this case we are dealing with multiple independent variables; therefore, other independent variables must constant to effect that change. The independent variables that showed positive coefficients were day’s, peoples while those that showed negative coefficients were shows and music, cost convenience and wine and food. The degree of coefficient varied: Days 25.43, People 13.76 Shows and Music = 1.42, Cost, 16.63 Convenience 17.65 and Wine and Food -2.45.On the other hand, people variable showed a P-value of 0.00 indicating a null hypothesis with regard to spending.

Table 5. Coefficients of Regression Data
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 127.46 19.31 6.60 0.00 89.31 165.62 89.31 165.62
Days 25.43 9.42 2.70 0.01 6.82 44.03 6.82 44.03
Peoples 13.76 2.39 5.76 0.00 9.04 18.47 9.04 18.47
Shows & Music -1.42 10.42 -0.14 0.89 -22.02 19.17 -22.02 19.17
Cost -16.63 11.15 -1.49 0.14 -38.67 5.41 -38.67 5.41
Convenience -17.65 9.06 -1.95 0.05 -35.55 0.25 -35.55 0.25
Wine & Food -2.45 10.42 -0.23 0.81 -23.05 18.15 -23.05 18.15

Discussion

The analysis showed that spending was a function of days – planned number of days in attendance and reason- what is the primary attraction to the festival. It revealed there is a positive correlation between the days- planned number of days in attendance and spending during the festivals. However, a null hypothesis was obtained between the number of people and spending during the festival and finally a negative correlation and coefficient of regression between the reason (primary attraction) to the festival and spending during the festivals. The analysis showed that the reason for going negatively affects spending given that all spending variables have negative coefficients with cost and convenience having the highest number of negative cost and convenience and p values of C=-16.63, p= 0.14 C =-17.65 and p= 0.05 respectively. Consequently, cost and convenience variables negatively affect spending greatest of all spending variables.

Conclusion

Following the analysis some of our original expectations were not met. The data showed that there is a positive correlation between the numbers of days and spending during the festivals, there is a negative correlation or negligible between the reason for going variables and spending during the festival and null hypothesis between the number of people and spending during the festivals. Therefore, further investigation should be carried out in order to determine the possible reasons for the null hypothesis in this case.

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