### time-series-analysis

Introduction:

Present study is based on the notion of time series analysis, the analysis of time series is useful in administration, planning, evaluation, of socio economic progress as well as for research in various scientific fields including pure sciences, econometrics and humanities. In the present study the significance of difference in net sale, gross profit made by company, Revenue generated across the months and season studied. finding significance of difference with respect to shop making amount of profit in relation to location of shop, number of sales occurred for different months of the year, average sales for different months of the year, Gross profit for different months of the year Total of 366 respondents were studied and data were collected using a pretested questionnaire.

Problem definition and business intelligence required.

In this study we try to investigate and tests the hypothesis

Number of sale of a product varies over a period of time, here we tests the hypothesis of whether difference in number of sales, Average sales, Gross profit varies over a period of month, In another hypothesis study is undertaken to test hypothesis of whether difference in number of sales and average sales varies between rainy days and Gross Profit.

• To test the significance of difference Analysis of variance and General Linear Model using post Hoc tests for multiple comparisons between categories of month and the season is studied. Bonferroni test is used for multiple comparisons and correlation is used to study relationship between the variables.
• Bar Chart, Scatter Diagram, box plot is used to visualize the data graphically.

To answer the aforesaid hypothesis following analysis is conducted.

1.0 What are my top selling products?

On the basis of quantity sold following are the top selling products are.

Natural Coconut Milk Icecream

Bar Graph Depicting Location wise Net Profit

3.0 What location in the shop makes the most amount of Profit?

Observed that maximum sales were observed from front location. 39074\$

Bar Graph Depicting Location Wise Maximum Sales

4.0 Is there a difference in number of Sales between different months of the year?

Solution:

Box plot representing distribution of data median at middle, third quartile at the top of box and first quartile at lower part of the box and dots represents the outliers these are the characteristics of boxplot, looking at the graph it is seen that median values for the month range in the tune of 1000.

Multiple comparisons using Post-Hoc Bonferroni test

 Multiple Comparisons Dependent Variable: Number of salesBonferroni (I) Month of the year (J) Month of the year February MeanDifference(I-J)-96.41-97.72-112.51-87.2347.14-29.32-44.15-24.37-63.13-207.76-98.8296.41 -1.32-16.11 9.18143.5467.08 Std.Error80.748 Sig.1.0001.0001.0001.0001.0001.0001.0001.0001.000 .6501.0001.0001.0001.0001.0001.0001.00 95% ConfidenceInterval Lower Bound UpperBound177.93172.01159.45182.50319.10240.40225.58247.60206.59 64.20170.91370.74273.02260.43283.51420.08341.42 JanuaryFebruary –370.74 March 79.391 –367.45 April 80.050 –384.48 May 79.391 –356.95 June 80.050 –224.82 July 79.391 –299.05 August 79.391 –313.88 September 80.050 –296.33 October 79.391 –332.86 November 80.050 –479.73 December 79.391 –368.54 January 80.748 –177.93 March 80.748 –275.65 April 81.396 –292.65 May 80.748 –265.16 June 81.396 –132.99 July 80.748 –

 MarchApril 52.2672.0433.27-111.36-2.4197.72 1.32-14.79 10.49144.8668.4053.5773.3534.59-110.04 -1.10112.5116.1114.7925.28 01.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.00 207.26 326.59348.58307.61165.18271.93367.45275.65257.17280.22416.82338.12323.30345.32304.31161.92268.63384.48292.65286.76297.25 August 80.748 –222.08 September 81.396 –204.50 October 80.748 –241.07 November 81.396 –387.90 December 80.748 –276.75 January 79.391 –172.01 February 80.748 –273.02 April 80.050 –286.76 May 79.391 –259.23 June 80.050 –127.10 July 79.391 –201.33 August 79.391 –216.16 September 80.050 –198.61 October 79.391 –235.14 November 80.050 –382.01 December 79.391 –270.82 January 80.050 –159.45 February 81.396 –260.43 March 80.050 –257.17 May 80.050 –

 MayJune 159.6583.1968.3688.1549.38-95.2513.7087.23 -9.18-10.49-25.28134.3757.9043.0862.8624.09-120.53-11.59-47.14-143.54 01.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.00 246.68 433.84355.15340.33362.33321.34178.94285.66356.95265.16259.23246.68406.33327.63312.80334.83293.82151.43258.14224.82132.99 June 80.703 –114.53 July 80.050 –188.78 August 80.050 –203.60 September 80.703 –186.04 October 80.050 –222.59 November 80.703 –369.43 December 80.050 –258.27 January 79.391 –182.50 February 80.748 –283.51 March 79.391 –280.22 April 80.050 –297.25 June 80.050 –137.60 July 79.391 –211.82 August 79.391 –226.65 September 80.050 –209.10 October 79.391 –245.63 November 80.050 –392.50 December 79.391 –281.31 January 80.050 –319.10 February 81.396 –

 July -144.86-159.65-134.37-76.46-91.29-71.51-110.27-254.90-145.9629.32-67.08-68.40-83.19-57.9076.46-14.83 4.96-33.81-178.44-69.49 01.0001.0001.0001.0001.0001.0001.000 .1141.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.00 420.08 127.10114.53137.60195.50180.68202.68161.69 19.28126.01299.05207.26201.33188.78211.82348.43254.90276.92235.92 93.53200.23 March 80.050 –416.82 April 80.703 –433.84 May 80.050 –406.33 July 80.050 –348.43 August 80.050 –363.25 September 80.703 –345.69 October 80.050 –382.24 November 80.703 –529.09 December 80.050 –417.92 January 79.391 –240.40 February 80.748 –341.42 March 79.391 –338.12 April 80.050 –355.15 May 79.391 –327.63 June 80.050 –195.50 August 79.391 –284.55 September 80.050 –267.01 October 79.391 –303.54 November 80.050 –450.40 December 79.391 –

 AugustSeptember 44.15-52.26-53.57-68.36-43.0891.2914.8319.78-18.98-163.61-54.6724.37-72.04-73.35-88.15-62.8671.51 -4.96-19.78-38.77 01.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.00 339.22 313.88222.08216.16203.60226.65363.25284.55291.75250.74108.35215.06296.33204.50198.61186.04209.10345.69267.01252.18233.20 January 79.391 –225.58 February 80.748 –326.59 March 79.391 –323.30 April 80.050 –340.33 May 79.391 –312.80 June 80.050 –180.68 July 79.391 –254.90 September 80.050 –252.18 October 79.391 –288.71 November 80.050 –435.58 December 79.391 –324.39 January 80.050 –247.60 February 81.396 –348.58 March 80.050 –345.32 April 80.703 –362.33 May 80.050 –334.83 June 80.703 –202.68 July 80.050 –276.92 August 80.050 –291.75 October 80.050 –

 OctoberNovember -183.40-74.4563.13-33.27-34.59-49.38-24.09110.2733.8118.9838.77-144.63-35.68207.76111.36110.04 95.25120.53254.90178.44163.61 01.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.000 .6501.0001.0001.0001.000 .1141.0001.00 310.73 90.79197.52332.86241.07235.14222.59245.63382.24303.54288.71310.73127.34234.04479.73387.90382.01369.43392.50529.09450.40435.58 November 80.703 –457.58 December 80.050 –346.41 January 79.391 –206.59 February 80.748 –307.61 March 79.391 –304.31 April 80.050 –321.34 May 79.391 –293.82 June 80.050 –161.69 July 79.391 –235.92 August 79.391 –250.74 September 80.050 –233.20 November 80.050 –416.59 December 79.391 –305.41 January 80.050 -64.20 February 81.396 –165.18 March 80.050 –161.92 April 80.703 –178.94 May 80.050 –151.43 June 80.703 -19.28 July 80.050 -93.53 August 80.050 –

 December 183.40144.63108.95 98.822.411.10-13.70 11.59145.9669.4954.6774.4535.68 -108.95 01.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.000 108.35 457.58416.59380.91368.54276.75270.82258.27281.31417.92339.22324.39346.41305.41163.02 September 80.703 -90.79 October 80.050 –127.34 December 80.050 –163.02 January 79.391 –170.91 February 80.748 –271.93 March 79.391 –268.63 April 80.050 –285.66 May 79.391 –258.14 June 80.050 –126.01 July 79.391 –200.23 August 79.391 –215.06 September 80.050 –197.52 October 79.391 –234.04 November 80.050 –380.91 Based on observed means.The error term is Mean Square(Error) = 97695.752.

Post hoc multiple comparison tests. Once it is determined that differences exist among the means using Analysis of variance, post hoc range tests and pair wise multiple comparisons can determine which means differ. Comparisons are made on unadjusted values. These tests are used for fixed between-subjects factors only. These tests of between-subjects effects help to determine the significance of factor. Hence, from the above table shows that number of sale do not differ significantly for months, P>0.5.

Analysis of Variance (ANOVA).

 Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 1399993.2 11 127272 1.303 0.221 Within Groups 34584296.4 354 97695.752

The differences between these months was not found statistically significant, F(11,354) = 1.303, p = .221 and we conclude that number of sale do not differ significantly with month.

5.0 Is there a difference in number of Average sales between different months of the year?

 Multiple Comparisons Dependent Variable: Average_SaleBonferroni (I) Month of the year (J) Month of the year MeanDifference(I-J) Std. Error Sig. 95% ConfidenceInterval Lower Bound Upper Bound January February .16 1.000 -3.35 3.66 March -1.68 1.022 1.000 -5.15 1.80 April -.02 1.031 1.000 -3.52 3.49 May -.21 1.022 1.000 -3.69 3.26 June .26 1.022 1.000 -3.22 3.73 July -.08 1.014 1.000 -3.53 3.36 August -1.59 1.014 1.000 -5.04 1.85 September 1.27 1.022 1.000 -2.21 4.74 October -.29 1.022 1.000 -3.76 3.18 November -2.43 1.022 1.000 -5.90 1.04 December -.40 1.031 1.000 -3.90 3.10 February January -.16 1.031 1.000 -3.66 3.35 March -1.84 1.022 1.000 -5.31 1.64 April -.17 1.031 1.000 -3.68 3.33 May -.37 1.022 1.000 -3.84 3.10 June .10 1.022 1.000 -3.37 3.58

 July -.24 1.014 1 -3.69 3.21 August -1.75 1.014 1 -5.2 1.69 September 1.11 1.022 1 -2.36 4.59 October -.45 1.022 1 -3.92 3.03 November -2.59 1.022 0.781 -6.06 0.89 December -.56 1.031 1 -4.06 2.95 March January 1.68 1.022 1 -1.8 5.15 February 1.84 1.022 1 -1.64 5.31 April 1.66 1.022 1 -1.81 5.14 May 1.47 1.014 1 -1.98 4.91 June 1.94 1.014 1 -1.51 5.38 July 1.60 1.006 1 -1.82 5.01 August .08 1.006 1 -3.33 3.5 September 2.95 1.014 0.256 -0.5 6.39 October 1.39 1.014 1 -2.06 4.83 November -.75 1 -4.2 2.69 December 1.28 1.022 1 -2.2 4.75 April January .02 1.031 1 -3.49 3.52 February .17 1.031 1 -3.33 3.68 March -1.66 1.022 1 -5.14 1.81 May -.20 1.022 1 -3.67 3.28 June .28 1.022 1 -3.2 3.75 July -.07 1.014 1 -3.51 3.38 August -1.58 1.014 1 -5.02 1.87 September 1.29 1.022 1 -2.19 4.76 October -.27 1.022 1 -3.75 3.2 November -2.41 1.022 1 -5.89 1.06 December -.38 1.031 1 -3.89 3.12 May January .21 1.022 1 -3.26 3.69

 February .37 1.022 1 -3.1 3.84 March -1.47 1.014 1 -4.91 1.98 April .20 1.022 1 -3.28 3.67 June .47 1.014 1 -2.97 3.92 July .13 1.006 1 -3.29 3.55 August -1.38 1.006 1 -4.8 2.04 September 1.48 1.014 1 -1.96 4.93 October -.08 1.014 1 -3.52 3.37 November -2.22 1.014 1 -5.66 1.23 December -.19 1.022 1 -3.66 3.29 June January -.26 1.022 1 -3.73 3.22 February -.10 1.022 1 -3.58 3.37 March -1.94 1.014 1 -5.38 1.51 April -.28 1.022 1 -3.75 3.2 May -.47 1.014 1 -3.92 2.97 July -.34 1.006 1 -3.76 3.08 August -1.85 1 -5.27 1.56 September 1.01 1.014 1 -2.43 4.46 October -.55 1.014 1 -3.99 2.9 November -2.69 1.014 0.553 -6.13 0.76 December -.66 1.022 1 -4.13 2.82 July January .08 1.014 1 -3.36 3.53 February .24 1.014 1 -3.21 3.69 March -1.60 1.006 1 -5.01 1.82 April .07 1.014 1 -3.38 3.51 May -.13 1.006 1 -3.55 3.29 June .34 1.006 1 -3.08 3.76 August -1.51 .997 1 -4.9 1.88 September 1.35 1.006 1 -2.07 4.77 October -.21 1.006 1 -3.62 3.21 Novembe -2.35 1.006 1 -5.76 1.07

 r December -.32 1.014 1.000 -3.76 3.13 August January 1.59 1.014 1.000 -1.85 5.04 February 1.75 1.014 1.000 -1.69 5.20 March -.08 1.006 1.000 -3.50 3.33 April 1.58 1.014 1.000 -1.87 5.02 May 1.38 1.006 1.000 -2.04 4.80 June 1.85 1.006 1.000 -1.56 5.27 July 1.51 .997 1.000 -1.88 4.90 September 2.86 1.006 .308 -.55 6.28 October 1.30 1.006 1.000 -2.11 4.72 November -.84 1.006 1.000 -4.25 2.58 December 1.19 1.014 1.000 -2.25 4.64 September January -1.27 1.022 1.000 -4.74 2.21 February -1.11 1.022 1.000 -4.59 2.36 March -2.95 .256 -6.39 .50 April -1.29 1.022 1.000 -4.76 2.19 May -1.48 1.014 1.000 -4.93 1.96 June -1.01 1.014 1.000 -4.46 2.43 July -1.35 1.006 1.000 -4.77 2.07 August -2.86 1.006 .308 -6.28 .55 October -1.56 1.014 1.000 -5.00 1.89 November -3.70* 1.014 .020 -7.14 -.25 December -1.67 1.022 1.000 -5.14 1.81 October January .29 1.022 1.000 -3.18 3.76 February .45 1.022 1.000 -3.03 3.92 March -1.39 1.014 1.000 -4.83 2.06 April .27 1.022 1.000 -3.20 3.75 May .08 1.014 1.000 -3.37 3.52 June .55 1.014 1.000 -2.90 3.99 July .21 1.006 1.000 -3.21 3.62 August -1.30 1.006 1.000 -4.72 2.11 September 1.56 1.014 1.000 -1.89 5.00 November -2.14 1.014 1.000 -5.59 1.30 December -.11 1.022 1.000 -3.58 3.36 November January 2.43 1.022 1.000 -1.04 5.90 February 2.59 1.022 .781 -.89 6.06 March .75 1.014 1.000 -2.69 4.20 April 2.41 1.022 1.000 -1.06 5.89 May 2.22 1.014 1.000 -1.23 5.66 June 2.69 1.014 .553 -.76 6.13 July 2.35 1.006 1.000 -1.07 5.76 August .84 1.006 1.000 -2.58 4.25 September 3.70* 1.014 .020 .25 7.14 October 2.14 1.014 1.000 -1.30 5.59 December 2.03 1.022 1.000 -1.44 5.50 December January .40 1.000 -3.10 3.90 February .56 1.031 1.000 -2.95 4.06 March -1.28 1.022 1.000 -4.75 2.20 April .38 1.031 1.000 -3.12 3.89 May .19 1.022 1.000 -3.29 3.66 June .66 1.022 1.000 -2.82 4.13 July .32 1.014 1.000 -3.13 3.76 August -1.19 1.014 1.000 -4.64 2.25 September 1.67 1.022 1.000 -1.81 5.14 October .11 1.022 1.000 -3.36 3.58 November -2.03 1.022 1.000 -5.50 1.44 Based on observed means.The error term is Mean Square(Error) = 15.416. *. The mean difference is significant at the 0.05 level.

Analysis of variance shows average sale is significantly different for months, now by using Post hoc multiple comparison Bonferroni tests, pair wise multiple comparisons can determine which means differ. Hence, from the above table shows that average sale do not differ significantly for months, P>0.5.

Boxplot showing month-wise distribution of average sale.

H1: Average Sale of month differ significantly and unequal.

Analysis of Variance (ANOVA)

 Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 335.651 11 30.514 1.979 0.030 Within Groups 5333.831 346 15.416

The differences in average sale between these months was statistically significant, F(11,346) = 1.979, p = .030 and we conclude that average sale differ significantly with month.

6.0 Is there a correlation between rain days and Gross Profit?

There is no relationship between Rainfall and Gross profit r=0.008, P=0.885 and correlation is found to be insignificant and very weak.

 Rainfall Gross Profit RainFall 1 0.008* Gross Profit 0.008* 1

P=0.885

Scatter plot between RainFall and Gross Profit

 Multiple Comparisons Dependent Variable: Net_SalesBonferroni (I)Season of the yearSummer (J) Mean Std. Sig.Season Difference Erro of the (I-J) r year 95% ConfidenceInterval Lower Bound Upper Bound Autumn -34.62 46.2 P>0.097 5 -157.44 88.19 Autumn Winter 55.00 46.297 P>0.05P>0.05P>0.05P>0.05 -67.82 177.82 Spring -33.65 46.423 -156.80 89.50 Summer 34.62 46.297 -88.19 157.44 Winter 89.62 46.1 -32.86 212.10 70 Spring .98 46.297 P>0.05P>0.05P>0.05P>0.05P>0.05P>0.05P>0.05 -121.84 123.79 Winter Summer -55.00 46.297 -177.82 67.82 Spring Autumn -89.62 46.170 -212.10 32.86 Spring -88.65 46.297 -211.47 34.17 Summer 33.65 46.423 -89.50 156.80 Autumn -.98 46.297 -123.79 121.84 Winter 88.65 46.297 -34.17 211.47 Based on observed means.The error term is Mean Square(Error) = 98056.709.

Post hoc multiple comparison test reveal that there is no significant difference in average sale across the categories of months, Bonferoni test is employed for multiple comparison. Statistical significance is tested at 5% level of significance. Results are not statistically significant here we fail to reject the null hypothesis.

Boxplot showing distribution of month wise number of sale

Hypothesis:

H0: Mean average sale equal for all groups (i.e., µ1 = µ2 = µ3 = … = µ12)

(ANOVA TABLE)

 Source of Variation Sum of Squares df Mean Square F Sig. Between Groups 855.940 3 285.313 1.138 0.334 Within Groups 90773.03 362 250.754

Results of the analysis of variance reveals that there is statistically significant difference were observed in determining the number of sale across the months, F(3,362) = 1.138, p = .334 and we conclude that number of sale do not differ significantly with month.

 Multiple Comparisons Dependent Variable: Average_SaleBonferroni (I) Season of the year (J) Season of the year MeanDifferen ce (I-J) Std. Error Sig. 95% ConfidenceInterval Lower Bound Upper Bound Summer Autumn -.56 .603 1.00 0 -2.16 1.04 Winter -.40 .598 1.00 0 -1.99 1.19 Spring -.40 .601 1.00 0 -2.00 1.19 Autumn Summer .56 .603 1.00 0 -1.04 2.16 Winter .16 .594 1.00 0 -1.41 1.74 Spring .16 .597 1.00 0 -1.43 1.74

1.0 Is there a difference in number of Average sales between different Seasons?

 Winter Summer .40 .598 1.00 0 -1.19 1.99 Autumn -.16 .594 1.00 0 -1.74 1.41 Spring .00 .593 1.00 0 -1.57 1.57 Spring Summer .40 .601 1.00 0 -1.19 2.00 Autumn -.16 .597 1.00 0 -1.74 1.43 Winter .00 .593 1.00 0 -1.57 1.57 Based on observed means.The error term is Mean Square(Error) = 15.973.

Multiple comparison using bonferroni post hoc test was conducted the results shows that the average sale do not differ significantly among the season of the year from Jan-Dec all p values are greater than 5%. Hence comparison shows with respect to season shows the insignificant results.

Descriptive statistics for season-wise average sale.

 Season of the year Statistic Summer Mean 18.18 SD 3.5 Autumn Mean 18.74 SD 18.74 Winter Mean 18.58 SD 5.3 Spring Mean 18.58 SD 3.9

Boxplot Showing distribution of average sale for season.

 Source of Variation Sum of Squares Df Mean Square F Sig. Between Groups 15.148 3 5.049 0.316 0.814 Within Groups 5654.334 354 15.973 Total 5669.483 357

(ANOVA TABLE)

Using analysis of variance determine whether there are any statistically significant differences between the means of two or more Season. The differences between these season was not statistically significant, F(3,354) = 0.316, p = .814 and we conclude that Average sale do not differ significantly with season.

9.0 Is there a difference in number of Gross Profit between different Seasons?

Post Hoc tests of Multiple comparision.

 Multiple Comparisons Dependent Variable: Gross_SalesBonferroni (I) Season of the year (J)Season of the year MeanDifferenc e (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound Summer Autumn -22.94 48.08 9 P>0.05 -150.51 104.63
 Winter 58.78 48.08 9 P>0.05 -68.79 186.36 Spring -46.44 48.22 0 P>0.05 -174.36 81.48 Autumn Summer 22.94 48.08 9 P>0.05 -104.63 150.51 Winter 81.72 47.95 7 P>0.05 -45.50 208.95 Spring -23.50 48.08 9 P>0.05 -151.08 104.07 Winter Summer -58.78 48.08 9 P>0.05 -186.36 68.79 Autumn -81.72 47.95 7 P>0.05 -208.95 45.50 Spring -105.23 48.08 9 P>0.05 -232.80 22.35 Spring Summer 46.44 48.22 0 P>0.05 -81.48 174.36 Autumn 23.50 48.08 9 P>0.05 -104.07 151.08 Winter 105.23 48.08 9 P>0.05 -22.35 232.80 Based on observed means.The error term is Mean Square(Error) = 105796.319.

By using Post hoc tests it is found that gross profit do not differ significantly across the categories of season when multiple comparisons is employed, Bonferoni test is used for multiple comparison.

Statistical significance is tested at 5% level of significance all P Values are found to be greater than 0.5

Descriptive statistics for Gross profit of different season.

 Season of the year Statistic SE Summer Mean 31.42 SD 31.67 Autumn Mean 19.73 SD 16.62 Winter Mean 27.64 SD 18.72 Springs Mean 44.211 SD 41.36

(ANOVA TABLE)

 Source of Variation Sum of Squares Df Mean Square F Sig. Between Groups 28591.757 3 9530.586 11.456 0.000 Within Groups 301149.197 362 831.904 Total 329740.954 365

There is significant difference in mean gross profit across the season, F (3,362) = 11.456, p = .000 and we conclude that Gross profit differ significantly.

Boxplot depicts the distribution of data and median values and outliers indicated by asterisks pertaining to gross profit

Results:

Following hypothesis was tested and these hypotheses along with significant/insignificant findings are stated below.

 Hypothesis Supported/ Not Supported P Value Whether there is a difference in number of sales between different months of the year. Not Supported P.0.05 Whether a difference in number of average sales between different months of the year. Supported P<0.05 Whether there is a difference in number of gross profit between different months of the year Supported P<0.05 To study relationship and correlation between rainy days and Gross Profit Correlation is weak P>0.05(r = 0.08) Whether there is a difference in number of sales between different seasons Not Supported P>0.05 Whether there is a difference in number of average sales between different seasons. Not supported P>0.05