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Use the data in the attached for this question. You are working as an analyst for a large cable company that offers bundles of channels

Use the data in the attached for this question.

You are working as an analyst for a large cable company that offers bundles of channels all across the United States. One of the bundles is the "basic package," which includes network channels along with a few other basic cable channels. You are interested in learning how the price of this basic package influences the rate of subscriptions in a market. You have data on subscriptions per 1,000 local residents, price for the basic package, and average local household income. You also have data on local telecom labor costs per subscriber. You believe this last variable influences the local price but not subscriptions per se.

  1. Based on the data provided, write out an expression for the data-generating process for subscriptions per 1,000 local residents.
  2. Estimate the effect of basic package price on subscriptions per 1,000 local residents using OLS. Why might you distrust this result as being a causal effect?

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Subs per 1000 Price Income Labor
440.708856 41.97364267 67.867 12
475.0794336 41.42173893 64.549 6
426.0134086 36.22490144 53.664 6
437.3416207 45.65210345 60.429 12
424.3132453 40.60737421 52.669 8
405.8547974 29.82663289 60.895 6
392.3133087 40.36838478 61.103 15
477.0864377 50.37490628 65.837 12
487.1057145 49.38095242 56.82 8
488.8287287 50.30028811 68.027 9
489.1651806 46.83036343 55.183 8
517.795371 48.89806183 62.407 6
508.5574657 57.29174428 66.807 13
455.5854772 48.62991287 62.806 12
442.4767971 49.97813285 53.608 13
452.0480126 44.11633544 59.35 11
505.8553432 48.00172386 64.845 7
424.0854643 43.58741072 53.561 12
450.9913707 49.84456178 57.924 13
440.1421517 49.66985861 64.123 14
458.4030341 38.56600568 60.007 6
524.0989899 50.31699832 67.197 7
449.6943836 44.27739727 52.03 9
473.3537491 44.87195818 63.122 7
440.6714648 38.62957746 63.894 6
460.3150734 47.3636789 56.133 12
463.3133672 40.45739453 68.569 7
483.3185748 53.26842913 64.708 13
485.1825862 45.0945977 63.615 6
455.6776429 53.67777382 61.611 15
444.993757 37.22762617 54.628 6
458.1288704 45.72864507 60.757 11
455.5963425 49.25505708 68.066 14
542.7305048 54.37108414 60.504 5
464.5800542 44.3266757 55.62 6
451.3592229 48.71020381 62.098 15
501.7435013 45.48425022 66.838 6
496.0710399 52.38383998 58.768 10
528.0587313 52.38945522 62.722 6
503.9196202 54.50327004 56.9 9
447.3272049 42.92753415 55.762 10
472.0317233 50.30328722 57.212 12
467.9481011 51.18801685 51.82 12
512.8771418 56.2321903 65.484 11
462.8304808 43.17508014 52.78 5
457.3451212 51.56818687 50.936 15
452.2986257 49.56160428 64.929 15
403.7495937 42.10576561 61.115 14
457.4643151 38.84921918 67.369 5
439.6837281 42.25695468 49.142 7
427.1804167 38.33690279 53.159 9
436.1152505 45.97287509 63.278 14
463.4571324 52.73018873 54.076 14
469.2879976 52.2009996 54.082 12
469.6511059 44.23335099 70.251 7
463.387035 39.59050584 66.844 7
540.5173261 55.17422102 54.472 7
494.7101662 55.8745277 59.463 13
519.1608019 63.39346698 61.8 15
449.3304619 45.92524365 60.779 10
426.4762936 43.62154894 60.747 14
470.9543456 44.09272427 54.398 7
486.1558392 53.03447319 52.949 11
428.2706986 48.84728311 56.187 15
475.3330935 56.72501559 62.983 15
450.2224818 46.57191363 59.791 13
462.3126544 40.2769424 57.651 6
485.341395 56.41939917 62.825 15
384.7280268 42.4148378 54.239 15
460.0327308 50.92345513 67.492 13
424.4351347 40.58668911 51.915 11
441.0487153 39.56661922 49.649 7
459.7077877 43.77363129 50.066 7
503.7665327 53.27542212 65.114 10
537.3140167 52.91250278 67.839 5
428.3412426 44.55487376 67.012 15
444.8506978 37.77728297 57.187 6
466.6000753 46.92117922 52.073 9
424.2793584 41.50905974 57.225 10
455.6276356 55.54143927 51.379 15
493.237391 51.26056517 64.674 12
476.5030929 41.13268214 67.707 6
433.9799887 35.01216479 61.907 5
518.6142563 48.78370938 68.912 5
477.0363682 50.10739469 63.392 10
519.3980672 54.0525112 67.083 11
455.0285791 44.57359652 50.587 9
434.2688435 36.11814059 52.56 5
454.4045715 48.08576192 55.89 11
475.8695755 45.07876258 63.397 6
452.4523826 46.70973044 53.194 12
422.5947251 36.03695418 59.373 8
456.9028192 41.9613032 65.135 8
398.5721638 36.86269396 60.396 10
416.4805602 37.75226003 52.967 7
462.1727125 40.56161875 58.803 7
475.0905822 47.37826371 54.821 9
506.0490929 50.93268215 69.453 9
459.4490199 46.20583664 55.214 9
542.0293132 61.93388554 58.426 10
455.5305572 37.36325953 64.351 6
504.2161787 47.73219644 62.823 7
455.8070895 42.50201492 60.795 8
468.7930457 49.63534095 54.981 10
407.8625937 37.92093228 69.337 10
388.1759727 33.27516212 51.525 10
478.7805063 40.49408438 65.816 5
372.6194419 38.29507365 51.849 14
459.2343691 48.15256151 67.319 12
419.9634728 42.90141213 58.555 11
492.1801672 49.53152787 68.991 11
418.7865803 41.70893006 55.533 12
491.0079192 46.12015319 57.287 6
476.9268646 49.09697743 64.345 10
426.2766255 48.65293758 63.359 15
452.4921531 47.87685885 52.231 13
468.7354236 49.27390393 67.092 13
423.3410046 39.16050077 58.378 9
457.1469203 53.17415338 53.102 14
433.2557233 51.22295388 52.918 15
417.3963591 41.04922652 59.101 13
465.0585272 38.20625454 66.821 5
482.8881377 42.95718961 60.145 5
381.4898903 33.46031505 54.728 9
461.6202159 49.61386931 61.937 11
418.0751401 39.57119001 69.648 13
479.6254035 43.78556725 61.912 7
397.4317606 35.01512677 55.341 9
485.3607692 45.76879487 69.748 7
423.0238697 39.90031162 54.622 8
422.0467217 31.90428695 54.621 5
444.4458418 38.92280697 58.909 7
434.2189267 41.29698779 55.437 9
473.3161115 43.39718526 61.933 6
445.816935 50.46282251 63.04 14
426.1656261 40.62410434 63.421 12
490.5561512 43.3355252 59.543 5
416.5152045 36.85236742 63.401 9
494.6223731 47.36689552 62.421 6
448.8182531 46.20020885 68.617 11
537.0895936 48.9237656 66.547 5
410.0478949 35.84498248 64.978 10
526.6479534 55.99132557 67.7 10
430.1305341 45.74742234 52.646 12
471.4404789 56.82441314 50.494 14
501.7190323 53.60583872 70.084 13
424.1284307 36.33673845 53.108 7
462.5100908 42.27468179 67.862 8
453.1058117 42.81546862 62.213 8
441.1548316 43.19663859 54.975 8
396.4919676 32.82866127 54.52 9
456.2877384 49.64812307 68.399 15
432.514367 39.42906117 57.94 8
476.7206459 48.80860765 50.869 8
496.0396507 47.88760845 63.714 6
493.3903821 43.72723035 55.027 5
419.7498283 42.40280472 60.333 13
500.2342313 50.92837188 61.664 9
519.0706379 50.80727298 64.227 6
467.8400159 43.70000265 63.64 6
480.9888719 39.99697864 66.007 5
496.3774711 50.64157852 61.528 10
427.1513732 39.94739554 55.467 9
472.3866943 48.17478238 50.338 8
445.8075013 40.90658355 63.368 7
529.4489975 52.86199958 68.277 9
427.8311596 44.19269327 58.675 13
441.1062786 45.32304643 54.168 11
489.926808 49.64213467 57.074 8
423.8769483 45.90349139 52.456 12
423.623731 40.42012183 54.103 11
442.3048419 42.59847365 63.714 11
472.6381137 54.38068562 62.354 15
379.09552 39.15108667 60.189 14
474.8429762 54.35332937 61.723 13
400.7194357 38.99473929 53.751 13
477.60119 42.87936499 66.325 7
403.3158446 34.02280744 52.179 7
461.7008374 40.8784729 57.43 5
480.1768286 50.2601381 50.616 8
453.0300655 49.32534426 55.078 14
478.0256816 42.78544694 60.313 6
398.9652489 42.44904148 51.271 14
457.1494159 50.60273599 67.533 14
483.4363334 55.40705557 55.994 12
486.2939531 44.06299218 52.916 6
370.851439 38.14207316 51.999 15
405.9808525 38.17197542 70.949 12
437.2217074 45.73528456 61.81 12
451.3719343 40.58948906 54.835 5
451.1899334 50.89915557 49.795 15
461.2608453 48.05964088 51.903 11
482.1830139 49.53183565 59.992 10
432.4264624 38.8924104 65.072 8
514.3450944 49.6426824 66.489 5
416.7543828 38.16956379 68.737 12
454.5808721 51.32631202 55.623 15
447.5880397 38.06767328 55.182 5
498.3487933 51.08596556 58.833 8
449.8146864 45.63178107 63.024 10
479.0455545 42.79775908 54.259 6
423.4818154 39.94146924 63.833 11
412.1426444 36.64110741 61.296 9
425.3230038 36.97450063 52.476 6
460.2404761 46.70074601 68.036 10
478.3965687 40.41509478 60.906 5
512.7050302 49.98150504 57.816 7
506.3577401 53.80545668 59.525 10
425.3642909 41.53588181 68.149 11
492.387905 59.85215084 54.275 14
523.8199279 50.59398798 67.256 8
467.6369845 45.20649742 66.398 10
413.6776968 42.99411613 64.713 14
444.4216102 38.38926837 55.086 5
461.7966544 53.2279424 54.429 13
504.4381171 44.64185286 70.587 6
533.6265854 55.9359309 69.011 10
425.6497289 47.78745482 53.925 15
447.2054102 52.63356836 53.404 15
455.2392378 53.04637296 65.961 15
404.0376518 31.37477531 54.789 7
467.8131462 47.56452437 52.426 10
470.1276946 49.51578244 51.033 10
449.7165249 45.17558748 53.663 9
447.2107925 50.10379874 49.588 12
435.8961795 40.20902992 66.642 11
450.9909966 46.44333277 59.331 12
421.8467039 35.78445065 50.14 6
468.5864518 44.87690863 57.325 7
418.6925325 42.33142209 70.704 12
439.314655 33.6174425 62.61 5
464.8225484 45.91125806 50.355 9
414.6686329 46.47893882 51.795 15
435.8472084 47.02203473 52.715 12
457.1433007 40.95605012 66.407 6
458.9141683 42.52202804 59.782 9
479.6872017 48.54320028 60.428 10
512.5798511 47.52597518 64.424 5
463.3355918 52.08926531 55.8 13
442.7725281 50.60008802 67.172 15
454.191332 42.01755534 51.086 8
445.8711615 47.81136024 60.003 14
476.6797618 46.7129603 64.402 9
509.1485902 55.18609837 70.032 11
449.7843498 49.71505831 56.494 12
439.7286993 45.12228321 55.995 13
447.5955457 48.17109094 52.569 13
479.0418562 55.9216427 60.512 15
424.1577108 45.9709518 61.332 14
452.6748431 41.82780718 49.708 5
446.2972998 37.55254997 62.982 7
432.989393 44.26273216 62.413 13
425.7505609 41.83042681 65.768 12
424.8970351 37.54833918 65.607 8
469.5451324 48.55402207 59.221 9
423.7235763 43.23742939 59.299 14
369.4439512 35.1813252 68.356 15
442.5367816 40.88379693 51.234 7
512.3080808 55.18868013 64.176 10
482.2746485 53.53410809 56.07 11
472.7297394 40.20262323 55.514 5
465.2472807 43.51338011 67.167 9
474.6769172 47.98131953 61.789 10
487.5959692 48.87582821 52.341 7
517.6538901 51.49814835 66.665 6
491.1074654 45.8914109 56.759 7
446.1241642 41.36052736 66.961 10
474.0933649 55.88556082 54.78 15
450.101675 42.16777916 64.095 8
449.3841444 41.0753574 49.932 5
430.2180193 40.68916989 66.083 12
470.8794423 41.86440705 67.693 7
435.1151863 40.64519771 68.244 10
420.1352534 40.6032089 65.516 11
445.9559329 49.46248882 61.181 13
452.8227664 50.6757944 53.768 15
420.2913057 32.51621762 54.194 5
466.2945989 52.84226649 65.241 15
459.0844852 50.43158087 56.495 12
431.3004112 44.46473521 53.512 10
417.8790295 44.02567158 56.725 15
441.4679363 43.28232272 59.774 11
434.6765205 49.42942009 55.1 15
461.2455874 49.30776456 54.399 11
473.3100828 45.84401381 62.246 7
439.1421717 47.41886196 60.629 15
469.2295683 51.73759472 53.804 13
472.6090082 47.1063347 56.971 9
452.2349821 50.36049702 64.072 14
458.8086519 52.33560864 65.795 14
449.9397859 40.03679764 64.719 9
440.2493414 45.02539024 56.097 12
417.3031799 38.04769664 51.017 8
448.3612184 49.33420306 59.356 13
454.2643038 51.64488397 63.395 14
480.2428535 50.94630892 54.565 12
500.8637526 54.4672921 69.06 13
422.1831134 42.44535223 66.511 13
450.2898605 43.92664342 52.73 8
445.9667724 45.6877954 61.84 10
451.2143642 43.34139403 64.166 11
496.6747015 45.14011692 62.834 6
416.4393848 45.82823079 57.47 15
406.9956043 34.58960072 50.458 6
438.5189621 48.83849369 64.488 14
428.9806967 40.29844945 51.19 10
501.8307634 43.82562723 70.877 5
447.4278889 43.68998148 62.288 10
457.2901081 47.66968469 60.272 11
416.1933836 34.16739726 59.189 5
459.0636394 38.88160657 58.774 6
436.4194459 41.12890765 66.646 11
439.2728045 49.04763409 52.987 14
486.7455045 48.19891742 65.552 8
466.9040283 45.09333804 69.344 8
443.687212 35.812202 67.814 7
480.7993191 47.53005318 65.619 10
448.9369832 43.46516387 57.146 9
423.0552892 43.36571487 59.861 12
471.8501274 44.65502124 51.92 5
502.4507911 48.44113185 69.804 9
426.0831482 47.4530247 52.365 15
515.5813409 59.99989015 62.582 14
498.1837511 59.50845852 63.133 15
457.501752 52.945792 60.827 14
507.5211549 49.22119248 67.194 9
501.9208529 53.71497548 49.631 10
412.5109656 43.92316094 66.972 15
476.8986107 55.63426845 66.093 15
402.1645293 34.86075488 48 6
476.9366313 44.22527189 51.585 7
448.8873296 45.39538826 55.515 11
490.2612304 45.5915384 67.712 7
477.2890008 56.23066679 61.905 15
435.5037136 49.5102856 68.442 15
457.6364448 45.81974079 63.718 12
464.3372692 41.85237821 58.223 7
451.6673761 49.02672935 49.507 12
427.9289428 40.65549046 50.996 8
516.9114572 52.64640953 64.033 7
490.0823559 49.03289264 51.885 9
482.3098648 42.55781081 58.963 5
475.8937064 52.7792844 68.218 14
504.0270847 54.42868078 66.455 11
433.6591081 35.57118468 68.232 5
403.6237989 36.83779982 55.597 11
419.920381 42.25623017 59.383 13
415.0138413 35.12097355 56.288 7
425.5204989 35.16141649 66.552 6
423.7230904 48.79251507 59.968 15
414.5475113 38.57425188 54.102 11
531.0636193 56.78943654 52.327 9
444.42254 44.37259 55.187 10
428.9576557 42.08710929 49.435 9
462.2743585 54.48272642 55.378 14
395.0007912 40.14129854 60.153 15
490.0360629 54.66734381 65.032 14
422.2640867 45.16318112 58.285 14
431.4353151 49.55755252 56.09 15
455.6376175 53.42060291 64.114 15
489.8009098 50.06565163 60.407 11
446.8263264 41.7845544 50.119 8
402.9290553 35.24234254 53.475 8
465.1457869 54.21846448 62.835 15
436.5993426 38.08389044 55.096 5
390.427114 36.63368566 50.625 12
497.050905 45.62398416 62.307 6
439.2056403 39.30794006 54.358 7
492.3705222 48.42908703 59.796 7
467.5738431 56.24480719 52.105 14
460.0843491 39.34239152 65.03 7
445.5181612 44.1643602 65.532 12
466.4252421 44.47754036 59.56 8
457.8702936 48.3377156 50.844 10
450.4706223 52.62760371 53.705 14
419.1195733 39.90392888 51.696 11
441.6711465 42.56119109 58.304 10
470.1833721 47.48422868 62.278 10
492.77977 47.573795 64.337 7
441.4486817 47.58244695 67.954 13
458.8569907 42.65249844 59.942 9
474.0964243 45.28757072 55.371 8
483.3222122 47.16520203 52.331 7
429.5886513 35.08044189 63.106 5
491.7566579 46.74494298 60.287 5
447.9079805 43.99083008 62.963 12
487.68588 49.78447999 58.979 10
497.144828 57.35847133 53.994 13
480.8277552 50.5339592 66.624 11
478.1161549 54.66285914 62.139 13
434.5745404 47.23575673 57.16 15
389.924451 39.08374184 50.422 13
430.1651254 40.11885423 64.452 10
455.206813 53.08280217 50.71 14
445.3204469 46.25707449 64.778 11
440.3215752 40.43976254 52.683 9
467.069324 50.442554 58.414 13
449.5554478 45.46907464 70.741 12
393.4591927 33.71453212 50.172 7
456.7267343 50.00978905 51.668 11
455.5242343 46.97203905 61.692 13
474.1820592 46.2553432 59.65 9
437.0019709 46.19566182 58.828 13
483.7121743 45.50519572 68.681 7
463.0884981 44.79391636 68.325 8
479.4908937 42.31598229 66.595 7
416.7711196 37.3076866 53.925 9
499.0007722 46.97996204 61.121 6
460.3496378 46.47693964 64.488 10
433.4672908 38.58904846 48.933 5
435.8826193 44.29110322 50.136 12
499.8866337 56.05327228 67.567 14
393.287535 35.36658917 58.088 10
454.0652076 41.86953459 51.848 6
434.8780009 50.73616682 58.461 15
451.0329368 38.79282281 51.276 6
507.8604665 46.47207775 58.028 5
481.146159 53.39219317 68.793 14
470.3755299 47.59592166 52.8 8
472.6409585 44.64065976 61.797 6
421.6142086 42.92353477 59.073 14
494.7021538 49.6511923 50.795 8
489.5756154 48.06826923 62.166 8
485.9583932 48.84723221 57.875 8
386.6755041 38.36908402 52.461 11
478.9159933 53.44066555 56.272 14
422.0910889 35.98151482 61.202 8
451.3667324 40.71162206 58.097 7
432.1659171 48.12331951 57.426 14
493.222909 53.61465149 60.535 10
399.2562311 36.00703851 54.214 11
438.9997776 44.51179627 57.929 12
415.8979642 33.3756607 53.644 5
486.9370209 58.80333682 57.117 15
475.6029335 54.45982225 67.844 14
466.0203813 39.28673021 54.3 5
456.3625275 39.23575459 67.948 7
438.8811597 43.43219329 61.288 11
433.7578739 45.04497899 53.488 11
458.5051078 50.46868463 69.693 13
513.2956125 48.21060209 65.032 7
420.1710396 45.45733993 56.427 15
457.1150961 43.06584936 66.72 9
434.7043692 40.10956153 53.047 7
417.468442 48.19607367 55.292 15
487.744436 46.36590601 65.549 9
449.6967492 43.68712487 51.574 9
462.7865809 45.22976348 60.408 9
424.047839 39.66763984 51.042 8
516.523621 51.04843684 66.233 6
400.4639964 38.06899941 53.05 12
425.9248315 47.71447192 48.638 15
481.6879413 50.29699022 55.906 10
387.1161808 38.81103014 54.25 12
395.3993645 43.34222742 56.346 14
482.0940941 48.64501568 53.224 10
440.2132534 36.37687556 51.952 5
469.1544404 47.0315734 55.965 9
413.6956197 37.66260328 60.72 9
458.5840163 44.12583604 49.829 6
468.4459387 50.50415644 63.421 14
498.3571715 52.77652858 60.698 11
415.8089902 39.8143317 51.923 10
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