I need to check if changes to a network architecture lead to an improvement in its performance, measured through the downlink traffic, in gigabytes (GB), and the user throughput, in megabits per second (Mbps). As shown in the chart below, the red points refer to the original architecture, while the green ones refer to the optimized architecture.
A visual inspection gives us hints that there is an improvement in the downlink traffic. The team responsible for the test measured such improvement using the following methodology: (a) calculated the linear regression for both data distributions (before and after); (b) for each traffic point of class "before", calculated the respective y-values by both regression equations; (c) weighted the difference between y-values and averaged the differences for all data points; (d) attributed this value as the percentage of improvement (~30%).
I particularly disagree with the effectiveness of this method since the $R^2$ (R squared or the coefficient of determination) is 0.51 for the before data (red line) and is 0.66 for the after data (green line), which means that both models are not able to represent the data distribution accordingly.
I have run statistical t-sample tests separately for each variable and only Traffic has a statistically significant difference. Does running statistical tests for each variable separately make sense?
What would be the best way to measure the distance between these both joint probability distribution?
As requested, I'm sharing the data I'm working with (exported using the dput R function):
structure(list(Traffic = c(358,634487359156, 358,081700458936,
364,921330559789, 368,123672707711, 387,53643531514, 379,257232916016,
362,713506327043, 359,82328383671, 381,305812425502, 407,339139784046,
428,416632881068, 412,655144067482, 376,046166926732, 363,07104534918,
358,815057027966, 282,870833084255, 361,876017556368, 345,019340467771,
325,154738267302, 353,44020143376, 385,570663061749, 399,900057155374,
380,75357941997, 358,444086059606, 385,568170535646, 414,561511115413,
440,586668527286, 411,941173812588, 408,46216126721, 416,850480920185,
370,807569426168, 317,450755503328, 401,90197103726, 357,792013536275,
381,27631753328, 382,546398056533, 408,533475208496, 413,183559601361,
374,583746472516, 377,47175338409, 382,34602665257, 424,172276348335,
443,576869009092, 426,001928981756, 404,514830761776, 393,723023576954,
380,731008211369, 341,872664736154, 396,601198857788, 385,935541188523,
380,291215827827, 393,249582091019, 416,597766468055, 414,589898218255,
391,348753989984, 370,381208988848, 379,26609523105, 414,334414292677,
436,208269479671, 415,150716591475, 395,087681618456, 390,461553170917,
351,186403941778, 301,609228907095, 297,733212342947, 306,126793995473,
341,63476696697, 344,649754236136, 379,451234531048, 411,316242129047,
365,386879046398, 354,853879155292, 362,501087713582, 402,304790950272,
414,95713039746, 402,312960896944, 369,086203204564, 355,598175144442,
328,091903332578, 287,513301425137, 399,676283700775, 396,413290084342,
396,906256358086, 398,282269240724, 439,290693427295, 438,40016924009,
385,792082463917, 389,526301987528, 397,595301351948, 445,665328936229,
475,42858313454, 458,958109118267, 425,770816422521, 416,327327385858,
364,511033068468, 317,879193045733, 417,47790512983, 417,448825658626,
394,080008704402, 406,029455790487, 451,495485965286, 442,415628792346,
416,22762634173, 417,579683279044, 423,085673441012, 449,121770273005,
466,044776250682, 468,675222131592, 455,624078507892, 434,903847485663,
384,542634517852, 303,480977536926, 419,506821377834, 400,548667836895,
395,717182933187, 384,060330716882, 428,07003327905, 438,640836482722,
416,389917485783, 418,902937692498, 417,281964883384, 431,67727244507,
478,636602703031, 449,204300581756, 426,873759223187, 418,234663749496,
376,283233853881, 327,534269853823, 410,116783178718, 404,865030679276,
394,724049754734, 403,219686503819, 441,379153354432, 433,10756700729,
403,84517208205, 395,899275812393, 421,981899798312, 455,844667068025,
452,339206051219, 480,922249139665, 456,455059015964, 420,062516225176,
408,752540558233, 348,543080009334, 431,440759412611, 410,560868246105,
432,150990878351, 399,035981439598, 454,710706164742, 457,529199292771,
425,425601557228, 405,04643119012, 418,493886464228, 447,466317519463,
466,141707821362, 461,292359813914, 448,354626127909, 445,544302946551,
405,518903360348, 372,891182774771), Throughput = c(11,5053501293553,
11,9309758603423, 13,7779263824406, 14,3917297378668, 14,1145090734722,
14,3385017873157, 15,5399892064479, 15,1220805389237, 12,7658038282802,
11,0769541704585, 9,73121702659838, 11,1248395386123, 13,9785700324735,
13,0841821644765, 16,8795922742222, 20,1712166512422, 9,85924113071211,
11,0171963969773, 12,889078970263, 12,0520743946818, 12,787965651558,
13,4985291104026, 13,6241787334508, 12,9393388194823, 10,6475688444511,
8,94585741419127, 9,07309002461651, 10,5375512217505, 13,4126520452011,
14,681020681011, 17,1688832173664, 20,390856149799, 10,9964196876543,
12,0536573820587, 13,0703310249279, 13,1021886458897, 11,9937017351554,
12,5364685320394, 12,8898704639515, 12,2924906025615, 11,7588259830951,
11,2093314898589, 9,44153033660997, 10,2496453925612, 12,1389408269939,
12,376784680386, 13,086556645542, 15,6967049567695, 10,1867216443261,
10,5959238812769, 12,8493064124163, 12,3358248820065, 11,9731228992546,
13,410871184402, 13,9815381338054, 13,9663018803019, 12,1306301432647,
10,5494236270779, 9,84281763667588, 10,3733162813883, 12,5014449363236,
13,8610332197323, 16,7369255368714, 20,1781422210165, 13,6150765560332,
14,0442640086184, 14,163977429003, 14,6742929846588, 13,0740906199482,
13,7559624325849, 13,5893530111571, 13,1089163422419, 11,5332502818746,
9,11523706352876, 8,3805330471852, 9,73240426713112, 12,799046563197,
14,8371428110662, 18,5229310449557, 20,435971290043, 12,0170507989659,
12,9058982111435, 13,8481714472943, 14,7156485298826, 13,287200295575,
13,5523506812201, 14,4592045748109, 14,2156223921772, 11,6292188916044,
9,92968406898798, 9,45360061535948, 11,4089857727813, 14,4388236123322,
15,909418885552, 18,1699248598878, 20,3621645035911, 11,7978070472534,
13,1508655077321, 14,3343464454511, 14,0502002112821, 12,7616484864157,
12,9440877816133, 14,2890334317849, 14,6643993135526, 13,2759215105139,
11,2692871367623, 9,77474917946549, 11,5132650662402, 13,9352357530285,
14,4083511053252, 16,6813231052547, 20,6856875487626, 11,6743340318485,
13,2820555865998, 14,1556667452738, 13,7909860283007, 13,3631836896703,
14,0503980847043, 14,9774350673516, 14,7544317206187, 12,8362467665561,
10,9958260673879, 10,2391581011887, 10,852961456615, 14,1156963140049,
15,1664041854793, 16,9983163274962, 20,2408680958295, 10,7083159850429,
11,6856128169095, 14,1340985422624, 13,9089185878862, 12,713960991684,
13,2529681935476, 14,5148070064275, 14,6163160719767, 13,1352335073843,
11,5100990914862, 10,2308474174595, 10,3750971421874, 12,7921209934226,
14,6289799709926, 16,1474606123663, 20,8216265897612, 11,4877393947863,
11,3850430887043, 12,8635532988091, 13,4561841980682, 12,0020124188846,
12,5788134443738, 13,8982334230915, 13,7057025833656, 12,9945455042547,
11,5904357008683, 9,78207049608405, 10,6653774524422, 13,0885353797632,
14,7293017960091, 15,5902490556672, 18,9172927752473), Target = structure(c(2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("After",
"Before"), class = "factor")), .Names = c("Traffic", "Throughput",
"Target"), row.names = c(NA, -160L), class = "data.frame")