INTRODUCTION

Kathy, VP, IOT Analytics has asked to perform an in-depth analysis of the power consumption dataset. As a part of the analysis, we explored the data via visualization and time series regression modeling. In this process.

Step: 1 :: Understand the importance of granularity and subsetting data into meaninful time periods.

Step: 2 :: Explore data using visualization techniques ans identify visualization that comtains most useful information and present toclient.

Step: 3 :: Develop atleast three time series regression models and eork with seasonal and non-seasonal forecasting.

Step: 4 :: Summarizing the analysis and make recommendations to client.

## Loading required package: lubridate
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## Attaching package: 'lubridate'
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## Attaching package: 'dplyr'
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Data Visualization

In this step,

I try to understnad how subsetting of data works by adjusting granularity and create visualizationsof data subsets. Visualization techniques are used to understand the data to find patterns and then perfrom regression analysis.

Exploring the importance of granularity

Data subsetting helps to adjust granularity and maximize the infromation gain.Granularity describes the frequency of observations within a time series data set.From the data description we know that the observations were taken once per minute over the period of almost 4 years. That’s over 2 million observations.

## Loading required package: plotly
## Loading required package: ggplot2
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## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
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##     last_plot
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##     filter
## The following object is masked from 'package:graphics':
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##     layout

## 
## Call:
## tslm(formula = tsSM3_070809weekly03 ~ trend + season)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.6235  -4.3795  -0.3765   0.6265  13.8735 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  8.615653   3.747160   2.299   0.0229 *
## trend        0.004865   0.008934   0.545   0.5869  
## season2     -4.504865   5.204442  -0.866   0.3881  
## season3      8.740270   5.204465   1.679   0.0951 .
## season4     -4.764595   5.204503  -0.915   0.3614  
## season5      0.230539   5.204557   0.044   0.9647  
## season6     -8.774326   5.204626  -1.686   0.0939 .
## season7     -0.279191   5.204710  -0.054   0.9573  
## season8     -4.284056   5.204810  -0.823   0.4117  
## season9     -0.288921   5.204925  -0.056   0.9558  
## season10     3.706214   5.205055   0.712   0.4775  
## season11    -6.548652   5.205201  -1.258   0.2103  
## season12    -4.303517   5.205362  -0.827   0.4097  
## season13    -4.558382   5.205538  -0.876   0.3826  
## season14    -4.813247   5.205730  -0.925   0.3566  
## season15    -8.818112   5.205937  -1.694   0.0923 .
## season16    -4.322977   5.206159  -0.830   0.4076  
## season17    -4.577842   5.206397  -0.879   0.3806  
## season18    -4.082708   5.206650  -0.784   0.4342  
## season19    -4.087573   5.206918  -0.785   0.4337  
## season20    -8.842438   5.207202  -1.698   0.0915 .
## season21    -4.097303   5.207501  -0.787   0.4326  
## season22    -4.102168   5.207815  -0.788   0.4321  
## season23    -8.607033   5.208144  -1.653   0.1005  
## season24    -0.361899   5.208489  -0.069   0.9447  
## season25    -2.116764   5.208849  -0.406   0.6850  
## season26    -8.871629   5.209225  -1.703   0.0906 .
## season27    -4.376494   5.209615  -0.840   0.4022  
## season28     1.618641   5.210021   0.311   0.7565  
## season29    -4.136224   5.210443  -0.794   0.4285  
## season30    -8.641089   5.210879  -1.658   0.0993 .
## season31    -8.645955   5.211331  -1.659   0.0992 .
## season32    -3.900820   5.211798  -0.748   0.4553  
## season33    -8.655685   5.212281  -1.661   0.0988 .
## season34    -8.660550   5.212778  -1.661   0.0987 .
## season35    -4.165415   5.213291  -0.799   0.4255  
## season36    -4.420280   5.213819  -0.848   0.3979  
## season37    -8.675146   5.214363  -1.664   0.0982 .
## season38    -8.430011   5.214921  -1.617   0.1081  
## season39    -1.934876   5.215495  -0.371   0.7112  
## season40    -4.439741   5.216085  -0.851   0.3960  
## season41     0.305394   5.216689   0.059   0.9534  
## season42    -4.449471   5.217309  -0.853   0.3951  
## season43    -0.954337   5.217943  -0.183   0.8551  
## season44    -5.709202   5.218593  -1.094   0.2757  
## season45    -3.964067   5.219259  -0.760   0.4487  
## season46    -8.718932   5.219939  -1.670   0.0969 .
## season47    -1.723797   5.220635  -0.330   0.7417  
## season48    -8.978662   5.221346  -1.720   0.0875 .
## season49    -0.483527   5.222072  -0.093   0.9263  
## season50    -8.778565   5.625186  -1.561   0.1207  
## season51    -8.783430   5.625519  -1.561   0.1205  
## season52    -5.788296   5.625867  -1.029   0.3052  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.36 on 152 degrees of freedom
## Multiple R-squared:  0.2569, Adjusted R-squared:  0.002673 
## F-statistic: 1.011 on 52 and 152 DF,  p-value: 0.4669

## 
## Call:
## tslm(formula = tsSM2_070809weekly02 ~ trend + season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.6667 -0.3333 -0.0264  0.0528 17.2805 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.4199825  1.2370651   0.339  0.73475    
## trend        0.0008249  0.0029633   0.278  0.78114    
## season2     -0.5008249  1.7015945  -0.294  0.76895    
## season3      4.4983502  1.7016023   2.644  0.00915 ** 
## season4      1.9975252  1.7016152   1.174  0.24246    
## season5     -0.0032997  1.7016332  -0.002  0.99846    
## season6     -0.5041246  1.7016564  -0.296  0.76748    
## season7     -0.0049495  1.7016848  -0.003  0.99768    
## season8     -0.2557745  1.7017184  -0.150  0.88074    
## season9      0.4934006  1.7017571   0.290  0.77230    
## season10    -0.2574243  1.7018009  -0.151  0.87999    
## season11    -0.2582492  1.7018499  -0.152  0.87961    
## season12    -0.4826766  1.8389826  -0.262  0.79335    
## season13     0.8498318  1.8388847   0.462  0.64470    
## season14     0.1823402  1.8387915   0.099  0.92115    
## season15     0.1815153  1.8387032   0.099  0.92150    
## season16    -0.1526430  1.8386196  -0.083  0.93396    
## season17    -0.4868012  1.8385408  -0.265  0.79158    
## season18     0.8457072  1.8384668   0.460  0.64624    
## season19     0.1782156  1.8383975   0.097  0.92291    
## season20     0.5107240  1.8383330   0.278  0.78157    
## season21    -0.4901009  1.8382733  -0.267  0.79017    
## season22    -0.4909259  1.8382184  -0.267  0.78982    
## season23    -0.4917508  1.8381682  -0.268  0.78947    
## season24    -0.4925757  1.8381228  -0.268  0.78912    
## season25    -0.4934006  1.8380822  -0.268  0.78877    
## season26    -0.4942255  1.8380464  -0.269  0.78842    
## season27    -0.4950505  1.8380154  -0.269  0.78807    
## season28    -0.4958754  1.8379891  -0.270  0.78772    
## season29     9.1699664  1.8379676   4.989 1.79e-06 ***
## season30    -0.1641919  1.8379509  -0.089  0.92895    
## season31     0.1683165  1.8379389   0.092  0.92717    
## season32    -0.4991751  1.8379317  -0.272  0.78634    
## season33    -0.5000000  1.8379294  -0.272  0.78599    
## season34    -0.5008249  1.8379317  -0.272  0.78565    
## season35    -0.5016498  1.8379389  -0.273  0.78531    
## season36    -0.1691414  1.8379509  -0.092  0.92681    
## season37    -0.5032997  1.8379676  -0.274  0.78462    
## season38     0.1625421  1.8379891   0.088  0.92966    
## season39    -0.5049495  1.8380154  -0.275  0.78394    
## season40    -0.5057745  1.8380464  -0.275  0.78360    
## season41    -0.5065994  1.8380822  -0.276  0.78326    
## season42     0.4925757  1.8381228   0.268  0.78912    
## season43    -0.1749159  1.8381682  -0.095  0.92433    
## season44    -0.5090741  1.8382184  -0.277  0.78224    
## season45    -0.5098991  1.8382733  -0.277  0.78190    
## season46     0.1559427  1.8383330   0.085  0.93252    
## season47    -0.5115489  1.8383975  -0.278  0.78123    
## season48    -0.5123738  1.8384668  -0.279  0.78090    
## season49    -0.1798654  1.8385408  -0.098  0.92221    
## season50    -0.1806903  1.8386196  -0.098  0.92186    
## season51    -0.5148486  1.8387032  -0.280  0.77989    
## season52    -0.5156735  1.8387915  -0.280  0.77956    
## season53    -0.1831651  1.8388847  -0.100  0.92080    
## season54    -0.5173234  1.8389826  -0.281  0.77889    
## season55    -0.1848150  1.8390852  -0.100  0.92010    
## season56    -0.5189732  1.8391926  -0.282  0.77823    
## season57    -0.1864648  1.8393048  -0.101  0.91940    
## season58     0.1460436  1.8394218   0.079  0.93683    
## season59    -0.5214480  1.8395435  -0.283  0.77724    
## season60    -0.1889396  1.8396700  -0.103  0.91835    
## season61     0.4769022  1.8398013   0.259  0.79586    
## season62    -0.1905894  1.8399373  -0.104  0.91765    
## season63     0.8085857  1.8400781   0.439  0.66104    
## season64     0.1410941  1.8402236   0.077  0.93900    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.406 on 138 degrees of freedom
## Multiple R-squared:  0.3234, Adjusted R-squared:  0.009581 
## F-statistic: 1.031 on 64 and 138 DF,  p-value: 0.4338

## 
## Call:
## tslm(formula = tsSM1_070809weekly01 ~ trend + season)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -19.506  -1.012   0.000   0.679  31.654 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  1.02656    5.15982   0.199   0.8426  
## trend       -0.01406    0.01119  -1.257   0.2111  
## season2      0.01406    7.20510   0.002   0.9984  
## season3      0.02813    7.20512   0.004   0.9969  
## season4      0.70885    7.20517   0.098   0.9218  
## season5      0.38958    7.20523   0.054   0.9570  
## season6      0.07031    7.20530   0.010   0.9922  
## season7      0.41771    7.20540   0.058   0.9539  
## season8     12.09844    7.20551   1.679   0.0956 .
## season9      0.44583    7.20564   0.062   0.9508  
## season10    12.79323    7.20579   1.775   0.0782 .
## season11     0.47396    7.20596   0.066   0.9477  
## season12     0.15469    7.20614   0.021   0.9829  
## season13     0.50208    7.20634   0.070   0.9446  
## season14     0.18281    7.20656   0.025   0.9798  
## season15     0.19688    7.20679   0.027   0.9782  
## season16     0.21094    7.20704   0.029   0.9767  
## season17     0.22500    7.20731   0.031   0.9751  
## season18     0.23906    7.20760   0.033   0.9736  
## season19     0.25313    7.20790   0.035   0.9720  
## season20     0.26719    7.20822   0.037   0.9705  
## season21    12.94792    7.20856   1.796   0.0748 .
## season22    12.96198    7.20892   1.798   0.0745 .
## season23     0.64271    7.20929   0.089   0.9291  
## season24     0.32344    7.20968   0.045   0.9643  
## season25     0.33750    7.21009   0.047   0.9627  
## season26     0.35156    7.21051   0.049   0.9612  
## season27     0.36563    7.21096   0.051   0.9596  
## season28     0.37969    7.21142   0.053   0.9581  
## season29     0.39375    7.21189   0.055   0.9565  
## season30     0.40781    7.21239   0.057   0.9550  
## season31     0.42188    7.21290   0.058   0.9535  
## season32    13.10260    7.21343   1.816   0.0717 .
## season33     0.45000    7.21398   0.062   0.9504  
## season34     0.79740    7.21454   0.111   0.9122  
## season35     0.47813    7.21512   0.066   0.9473  
## season36     0.82552    7.21572   0.114   0.9091  
## season37     0.83958    7.21634   0.116   0.9076  
## season38     0.85365    7.21697   0.118   0.9060  
## season39     0.86771    7.21762   0.120   0.9045  
## season40    16.88177    7.21829   2.339   0.0209 *
## season41     0.89583    7.21897   0.124   0.9014  
## season42     0.57656    7.21968   0.080   0.9365  
## season43    13.59063    7.22039   1.882   0.0621 .
## season44     0.60469    7.22113   0.084   0.9334  
## season45     5.95208    7.22189   0.824   0.4114  
## season46     0.63281    7.22266   0.088   0.9303  
## season47     0.64688    7.22345   0.090   0.9288  
## season48     0.99427    7.22425   0.138   0.8908  
## season49     0.67500    7.22507   0.093   0.9257  
## season50     1.35573    7.22591   0.188   0.8515  
## season51     0.70313    7.22677   0.097   0.9226  
## season52    13.71719    7.22765   1.898   0.0600 .
## season53    13.39792    7.22854   1.853   0.0661 .
## season54     1.07865    7.22945   0.149   0.8816  
## season55     0.75938    7.23037   0.105   0.9165  
## season56     1.44010    7.23132   0.199   0.8425  
## season57     0.28125    8.05864   0.035   0.9722  
## season58     0.29531    8.05896   0.037   0.9708  
## season59     0.30938    8.05929   0.038   0.9694  
## season60     0.32344    8.05964   0.040   0.9681  
## season61     0.33750    8.06001   0.042   0.9667  
## season62     0.35156    8.06039   0.044   0.9653  
## season63     0.36563    8.06078   0.045   0.9639  
## season64     0.37969    8.06119   0.047   0.9625  
## season65     0.39375    8.06162   0.049   0.9611  
## season66     3.40781    8.06206   0.423   0.6732  
## season67     0.92188    8.06252   0.114   0.9091  
## season68     0.43594    8.06300   0.054   0.9570  
## season69    19.45000    8.06348   2.412   0.0173 *
## season70     0.46406    8.06399   0.058   0.9542  
## season71     0.47813    8.06451   0.059   0.9528  
## season72     0.49219    8.06504   0.061   0.9514  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.824 on 127 degrees of freedom
## Multiple R-squared:  0.3207, Adjusted R-squared:  -0.06442 
## F-statistic: 0.8327 on 72 and 127 DF,  p-value: 0.8018

##          Length Class  Mode     
## x        205    ts     numeric  
## seasonal 205    ts     numeric  
## trend    205    ts     numeric  
## random   205    ts     numeric  
## figure    52    -none- numeric  
## type       1    -none- character

##          Length Class  Mode     
## x        203    ts     numeric  
## seasonal 203    ts     numeric  
## trend    203    ts     numeric  
## random   203    ts     numeric  
## figure    64    -none- numeric  
## type       1    -none- character

##          Length Class  Mode     
## x        200    ts     numeric  
## seasonal 200    ts     numeric  
## trend    200    ts     numeric  
## random   200    ts     numeric  
## figure    72    -none- numeric  
## type       1    -none- character