Statistics SPSS

Graph 13: Line Chart of Sales Trajectory of Variant 13

Graph 13 represents that the sales of variant 13 reduced in the 10th week from the initial years and the sales were highest at the 30th week which again declined followed by increase in sales. These findings present the normal performance of variant 13.

Summary Statistics of all Variants

The summary statistics of all 13 variants were analysed through SPSS and are presented in Table 1:

Table 1: Summary Statistics of Variants

Table 1 represents that the Variant 1 of weekly sales volume has the highest mean of 340863.05 followed by Variant 9 with mean 212244.64 while Variant 13 has the lowest mean value of 817.16. Table 1 demonstrates that Variant 1 has highest weekly sales from the remaining variants, the average sales of variant 9 are 212244.64 and variant 10 has average sales of 183583.33 while Variant 13 has lowest sales with mean value of 817.16 followed by variant 8 with mean of 1133.64. The median value of variant 8 is zero which indicates its reduced sales in a year. The standard deviation of all variants represents the dispersion of the sales and the variants with high standard deviation to their mean values has high dispersion while the low standard deviation values with mean indicate the low dispersion of sales data.

The minimum weekly sales of variant 1 are 276408 while the maximum sales are 407164 while the minimum weekly sales of variant 4 is 49, variant 5 is 16, variant 12 is 205 and variant 13 has minimum sales of 554 while the minimum sales of variant 8 is 0. These findings represents that variant 1 and variant 9 has highest weekly sales while variant 13 and variant 8 has lowest weekly sales in a year.

Part (b)

Top Four Selling Variants:

The top four selling variants from all thirteen variants are following:

· Variant 1

· Variant 9

· Variant 10

· Variant 2

The top 4 selling variants are presented in Figure 1 in a pie chart.

Figure 1: Top four Selling Variables

Figure 1 represents that these Variants has high sales based on their mean and maximum sales values. The average sales volume of variant 1 is 340863.05, variant 10 is 128618.41, variant 9 is 212244.64 and variant 2 is 183583.33. The maximum sales volume value of Variant 1 is 407164, Variant 9 has maximum sales value of 285225, and Variant 10 has maximum sales volume value of 252682, while Variant 2 has maximum sales value of 21848.

Question no 2:

Part (a)

Correlation Analysis

Correlation analysis determines the correlation between the different variables. The analysis also measures the strength of the correlation between variables. The correlation is significant at the level of 0.01 or less than 0.01 and less than 0.05. The correlation analysis was conducted for determining the relationship between the various prices. The correlation analysis is presented in Table 2:

Table 2: Correlation Analysis of Various Prices

Table 2 represents the significant correlation between various prices. The findings of correlation analysis are as follows: unit price of Variant 1 is significantly correlated with the unit price of Variant 9, 10 and 13. In addition, unit price of Variant 2 is significantly correlated with unit price of Variant 8, 11 and13. The unit price of Variant 3 is significantly correlated with unit price of Variant 6, 7, 8, 11 and12. While the unit price of Variant 4 is not significantly correlated with any of other variants. In addition, unit price of Variant 5 is only correlated with unit price of Variant 10. Moreover, unit price of Variant 9 is significantly correlated with unit price of Variant 1 and 10.

Part (b)

Closely Related Variant – In Terms of Prices

The correlation analysis in Table 2 has presented various variants that are closely related to each other in terms of their prices. The analysis demonstrated that prices of Variant 10 are closely and strongly related with prices of Variant 9.In addition, prices of Variant 11 are closely related with Variant 12. The prices of Variant 1 are closely related to prices of Variant 9. The prices of Variant 3 are closely related to prices of Variant 2 and Variant 8 and prices of Variant 7 are closely related with prices of Variant 8.

Methods for detecting and solving multicollinearity:

There are various methods for detecting and solving multicollinearity, some of these methods include:

Detecting Multicollinearity:

Variation Inflation Factor can be used to detect the multicollinearity between the variables. In addition correlation matrix and correlation plot method can be also used for detecting the multicollinearity

Solving Multicollinearity:

The methods which can be used to solve multicollinearity are as follows:

· The removal of one or more variables with a high correlation is a simple method of correcting multicollinearity. It significantly reduces the multicollinearity between correlated variables.

· Methodologies such as partial least squares regression and principal component analysis are also used for solving the multicollinearity.

· Through the breakdown of data into independent variables, PCA decreases the dimension of data. As a result, new variables with no association are generated.

· Centering the data can also solve the multicollinearity issues.

Part (c)

Exploratory factor analysis of Distribution Variants

Exploratory factor analysis is a statistical approach for reducing data into a smaller number of summary variables and exploring the phenomena's fundamental theoretical structure. It's implemented to find out how the relationship between the variable and the respondent is structured. The Exploratory factor analysis of Distribution variants is conducted through SPSS. KMO and Bartlett’s test is presented in Table 3:

Table 3: KMO and Bartlett’s test

Table 3 represents the findings of KMO and Bartlett’s test. The Kaiser-Meyer-Olkin (KMO) statistic evaluate the appropriateness of factor analysis and a high test statistic between 0.5 and 1 indicates that the data is appropriate for factor analysis. The Table 3 demonstrates the KMO value of 0.6 which represents the appropriateness of data. Bartlett's test of sphericity significant result of less than 0.05 indicates that the variables are sufficiently related to one another to conduct a useful exploratory factor analysis. The significance value of Bartlett’s test is 0.000 in table 3 which represents the sufficient relation of data.

The communalities of exploratory factor analysis are presented in Table 4:

Table 4: Communalities

Table 4 represents the communalities exploratory factor analysis and demonstrates the initial correlation of distribution variants. The most of variants have their relation values of 0.9 which demonstrates the high relationship of the variants.

The total variance explained is presented in Table 5:

Table 5: Total Variance Explained

Table 5 represents the distribution of variance among 13 possible factors. The initial Eigenvalues of four factors are higher than 1 and therefore only these four factors has high percentages of variance. The variance of first factor is 39%, the second factor has 27% variance, and third factor has 12% variance while the fourth factor has 10% variance. The remaining factors have less than 6% variances. The extraction sums and rotation sums only represents the data for first four factors.

The rotated component matrix is presented in Table 6:

Table 6: Rotated Matrix

Table 6 represents the rotated component matrix, in this tables the variants are loaded on four selected factors. The values are rotated on the basis of factors.

The transformation matrix is presented in Table 7.

Table 7: Transformation Matrix

Table 7 represents the transformation matrix of top four factors with high variance. This table presents the final findings of exploratory factor analysis. The screen plot of exploratory factor analysis is presented in Figure 2.