# QUESTION SUMMARY: –

In the sample solution presented below, the expert demonstrates our capability to solve a multipronged problem in statistics subject. The expert has demonstrated our prowess by performing various statistical operations on an excel database. Calculation of descriptive analysis, standard deviation, and analysis of the behavior of the variable of interest has been performed by the expert. Box diagram and histograms have been presented. In the sample a host of hypotheses has been corroborated and refuted.

SOLUTION: –

The Excel data base presented here encapsulates the information on the 32 teams that took part in the worldcups of 2006, 2010 and 2014. The assignment aims at making an analysis of “how the value of various football teams has emerged in the due course”.

The variables with greatest variability are Market Value, Home Continent, Home Country, Jugadores, Market Value, PTS, Ranking Fifa and Total goals. For all those variables the standard deviation is nearly as large or even greater in some variables, than the mean value. However, for some variables like Home Country, Home Continent for example the mean is not meaningful because those variables take only the values 0 and 1. The sample consists of young people with minimum age of 22.5 years, maximum of 28.29 and an average of 25.44. Jugadores, or the number of players is between 0 and 5, with an average of 0.3125, which again is not very meaningful since there cannot be less than 1 person. The average market value is 184 mil. EUR with a minimum of 0 and a maximum of 863.5 mil. EUR. The average total points are 5.55 with a minimum of 0 and a maximum of 19. The ranking can be between 0 and 103 and the mean value is not meaningful. The total goals are on average 4.86 with a minimum of 0 and a maximum of 18.

1. The variable of interest is total goals.

For 2006 on average there were 4.75 goals with a minimum of 0 and a maximum of 14. In 2010 the average number of goals was slightly lower, 4.53 with a slightly higher maximum of 16. The average number of goals in 2014 was higher than in the previous years, 5.31 as well as the maximum number of goals, 18.

3.

Market value is positively correlated with PTS, moderate correlation. It is negatively correlated with the Ranking variable, moderate correlation. Market value is positively correlated with Total goals, moderate correlation. That means that the higher market value is associated with lower ranking (the first places) and higher PTS as well as Total goals. The PTS is strongly positively correlated with Total Goals meaning that the higher total points are associated with higher total goals.

4.

All the observed variables have outliers which is very evident from the boxplots. Since they are only a few observations, it might be a solution to simply remove them from the sample. However, it should be checked whether those are the same observations for all the variables. Moreover, the possible reason for their presence should also be considered before deletion.

5.

In order to test the hypothesis that the variability of the market value has changed over the years variance equality test was used to test for significance difference between the three years with regard to variance in market value.

According to the results shown above, the null hypothesis that the variance in market value in each of the three years does not differ is rejected at the 5% significance level (F= 7.84 with p-value = 0.02). Therefore there is sufficient evidence to support the hypothesis that the variability of the value of the teams has risen.

6.

An independent samples t-test would be appropriate to test for significant difference between the European and Non-European players. For this purpose a dummy variable should be created to indicate with a value of 1 that a player is from European country and a value 0 if he is not. This will be the classifying variable and the dependent variable is total goals.

The results indicate there is no significant difference between the European and non-European players with regard to total number of goals at the 5% significance level (t=-1.19 with p-value = 0.24)

7.

Yes, the value of a term matches the quality. The quality can be measured by the ranking as well as by the total number of goals. From the correlation analysis it was evident that higher market value is associated with first rankings and higher total number of goals.