Instructions. Answer each question as briey and completely as possible on the excel le provided to you. Be sure to rename the Excel le with your last name before submitting it to Blackboard. Scenario: The following dataset contains survey responses of 500 heads of households in the Philadelphia area. The data contains information on their annual consumption expenditures and other information regarding the characteristics of their household. Your job is to construct the best regression model to explain how household characteristics impact consumption expenditures. The variables in the dataset are as follows...

Yi : Annual consumption expenditures of household i in thousands of US dollars.

X1i : Annual gross income of household i in thousands of US dollars.

X2i : Hourly wage rate of household i in US dollars.

X3i : Number of dependents in household i (i.e. number of children)

X4i : Average age of dependents in household i in years.

X5i : College education (1 = respondent has a college education, 0 = respondent does not have a college education)

1. Test your independent variables (X1i; :::; X5i) for potential multicollinearity. Report the variance ination factor (VIF) for each independent variable, and state your conclusion. If your test suggests that you should remove an independent variable from your analysis, then remove it before proceeding.

2. Run a regression with consumption expenditure (Yi) as your dependent variable and the remaining X variables as your independent variables. Check if any of the regression coe cients are insignicantly di?erent from zero. If so, remove the corresponding independent variables (one at a time) from your analysis and arrive at a model where all regression coe cients are statistically signicant. Only state your nal regression results.

3. Using your results from question 2, perform a residual analysis on your regression. Does there appear to be a pattern in any of the relationships between the residuals and your independent variables? If so, then extend your dataset by adding a nonlinear form of the independent variable in question (i.e. add a squared term). State your nal regression results which successfully pass a residual analysis.

4. Using your results from question 3, answer the following questions.

(a) What is the R2 value? What does this say in the context of the scenario? (b) Interpret each of the relationships between consumption expenditure and the independent variables. In the occurence of a linear and quadratic term, be sure to interpret both terms jointly and not separately. (c) Test the following hypothesis: For every $1 increase in income on average, a household will increase their consumption expenditure by MORE THAN $0.30. Be sure to state the null and alternative hypotheses, the p-value of the test, and your conclusion.

Consumption (Y) Income (X1) Wage (X2) No. of dependents (X3) 45.844556604 182.479159474 59.4392588826 57.9092551178 230.994547324 62.6947065552 64.4758098362 238.5421760995 70.1762210313 4.1461662223 34.9022123863 14.145493017 19.7257302905 56.6042023821 19.1629829954 9.4883622161 23.9069494629 25.9054220781 37.7250773799 140.4046770414 16.0709687355 40.4488196073 153.0235639988 34.9564396592 5.4171382791 36.5107679787 40.0090621808 13.8775120902 41.6543375362 37.3316108483 23.1305421503 72.3923150123 37.1533814785 51.8855757251 208.2616896802 37.7499867745 29.3348566951 101.4849627088 11.2567188876 17.2779278416 103.5506524198 44.813390543 19.4421989013 81.3713293048 45.2434655344 2.8893141158 18.5505236857 40.2666554603 32.3172402364 119.7216613319 45.8452181438 14.9063208641 51.531252572 16.0587960343 13.7265200048 81.0173073556 40.6266103555 7.2900663652 77.0443266001 17.5356890697 44.7669728197 150.3765600786 23.1918063013 8.4937679932 27.3152398884 34.5523120191 38.661393731 155.8844141165 34.4736072071 70.5852725037 245.373948302 42.3545324133 19.5615942967 88.6142150542 12.5251589757 40.8046217418 190.8433260235 29.4544686849 8.6313996069 30.3282233669 10.3780841138 35.1685744505 145.639048518 50.8059139629 50.2773615141 223.5576819813 36.4086486071 32.0511269534 133.1383373249 54.7321242171 26.7555969455 108.9420895209 22.3243802349 48.2613655403 201.9909385862 22.5381090837 22.9850085274 73.26177265 35.4483481726 16.4202756834 77.5643551652 19.3917681686 58.7053812826 210.541205468 61.0489717702 56.2412468707 206.3875175923 54.507388564 20.2655989959 67.7016878716 19.0347180997 0.8678725772 24.3858257935 6.1262088094 24.2321415664 75.2465040154 40.3214934587 44.4591703675 178.6695286023 57.9897522999 30.5193701124 145.2880011519 24.4060480946 32.4059744406 125.7513617822 20.620195082 -6.0305517683 28.9632309612 9.6577778145 8.6690327596 73.9321715859 43.2657810879 32.2930249621 144.7576355181 21.3092460155 10.0596047023 50.5664990985 35.4304555585 27.4921447787 139.6536812627 31.0315480643 4 2 4 3 4 3 4 2 3 2 1 3 2 4 3 1 3 2 3 1 2 3 1 3 1 2 3 1 3 4 4 3 1 2 2 2 3 2 3 1 2 1 4 1 2 2 2 38.9647390034 48.8583418208 61.4669935515 13.6310549427 34.9905422512 50.5905649878 40.6149517606 28.5068127303 33.3610756463 46.3927436346 24.6594952198 22.093902449 28.2807501141 14.9001893329 31.2537458728 12.5072312048 33.2858867338 33.8076417388 39.3692935343 2.6317329914 30.2578876308 37.1344966189 55.0960990556 61.2211727074 29.6552030932 46.3141276716 49.1983237033 39.0270743025 49.4707655317 57.1164253866 7.8597832289 6.1529876083 59.8679464188 33.2595015058 37.8490648409 -5.5122124531 28.2646420151 19.8179189663 40.1919545063 27.2884674762 44.6362428091 50.0924024336 14.7497629157 12.9864776361 23.3929946008 49.5369171603 40.1591769428 38.3695373444 166.417630636 154.3935532766 242.6641474277 90.9307068007 159.7017214624 187.3174893164 184.7953322476 102.9709724419 120.5767784878 202.4945682578 109.1603276155 123.7281898956 92.3072081876 53.2675523151 167.1538482323 122.3574797924 114.8614824118 141.7023058141 158.1834190439 18.4102550462 101.8715967504 193.5986055777 201.9039019863 225.8752966321 117.4983518271 163.0380567813 197.1923889915 166.3520907281 189.2459078649 216.4107719108 57.5645161275 19.5258830168 226.1465365746 119.2211520374 144.733603635 20.9360029313 107.8190461846 103.9054576593 165.5091058108 145.7492607865 144.3450374486 197.4511096037 36.9439979348 52.8886692257 75.7163012556 183.0243312172 217.0734633044 140.2063694054 29.3377328243 28.9528168852 39.7765738777 14.8098406048 19.8348360199 27.9788908189 32.8324385391 26.5437168459 19.3753166321 55.1580764621 19.5400780953 23.6220480846 41.5784680897 35.3809723689 56.9319160063 50.5684508267 18.6040986038 26.4988959708 50.7685111993 8.828938128 45.4738862329 37.3420771884 42.182275764 41.7184859768 34.8280574108 56.1589167863 50.3213343596 61.038598966 29.2003668887 64.1301036003 34.084706012 28.4168811246 62.8253441845 51.1094181743 46.4147935754 12.6609531258 13.228429705 18.6017709928 55.5994023122 25.0114830354 57.446662955 53.4671996428 29.4540080723 17.6548688094 40.8833949613 58.7874432918 50.4505462955 41.6636483856 4 2 1 1 2 2 3 1 4 3 3 1 3 4 3 3 4 4 4 2 2 1 3 3 2 4 1 2 3 4 1 2 2 3 2 3 2 4 4 2 4 2 3 4 1 1 3 1 44.6796257924 4.4272497775 47.195444323 30.0173156115 26.2994630662 65.41072696 -2.5604833727 31.0731023899 47.6361665854 16.3411426013 18.2710718302 40.6707801791 65.3649867381 52.755771984 14.1606800398 31.7295936554 35.5414109245 46.8077616527 27.6168982239 14.6568082295 55.4812404558 40.6949538471 59.7215658007 17.7036704613 31.8055495346 4.7224000372 58.6588152789 11.1980649099 14.5592573151 30.9350548154 10.0405849124 33.719751105 19.7867531859 57.020762485 55.1634551115 56.0230504765 20.670251713 45.8768729545 24.7807817399 36.4786425283 62.2376501299 42.4837450512 48.365191489 51.3190367717 45.7532213337 42.5505413407 24.4216903386 14.8013879318 139.7899124474 13.4623290641 203.3961432416 104.4954373545 92.947910356 249.0767724901 10.9803379262 142.52589994 165.6999476399 47.8840865864 40.5311082922 201.5517379258 246.4401718002 197.9484147622 80.9218696255 101.8457887829 144.9710254181 174.4563170896 111.24844908 57.418115744 197.3199037153 160.1452609664 201.014145835 75.6088177975 117.1073387647 19.4352014749 205.9306723973 16.4176684636 106.7303787638 137.409777318 36.5915789519 115.0792700873 87.0879480125 234.3237102429 216.910113209 221.1857193668 97.4468082976 162.8314624737 65.8934028427 139.3564885463 238.2645265617 204.3252042985 246.5288506586 204.7657610977 172.9474421045 159.2104305375 85.666108527 34.2586242856 26.6143858481 25.8569827429 51.1303902654 15.1203450173 24.4399870072 47.7584220393 27.8069047032 52.1391103187 49.8212290437 30.5168107154 9.8401637316 56.8786109279 36.7618078935 32.6380388712 33.2990377542 47.7662331317 51.5919313489 52.7108084521 17.4860183661 12.6272513662 59.3034142016 53.9187780212 57.9056852557 43.5690108457 43.8515401907 28.8208090367 44.4739601344 36.2404404949 45.5581103113 49.2330787848 11.8176372516 44.2899354789 43.7692598148 64.1947147966 66.3622596413 44.7561242839 43.7716029903 23.8925636375 13.4682689018 20.3390991753 68.3847128508 55.1226277101 37.8809789987 35.8574472009 54.2127145868 22.2257054364 46.5380400642 8.6369899587 3 1 2 4 2 3 1 2 3 3 4 1 3 2 4 4 4 4 1 3 3 3 4 4 3 1 3 1 3 3 2 1 4 2 4 4 1 1 2 2 4 3 3 1 2 4 1 1 62.6519412173 15.8125465225 34.7516497785 26.4339674293 55.6724934761 35.5320334361 44.5538200018 58.3440364198 40.7356776021 5.191678001 11.6606918185 53.2178099176 52.7064310089 27.1393602104 26.9278368108 29.1357341774 43.6043272759 51.7156255812 58.7777787418 -0.0321309014 37.3978977098 51.3464074204 33.7965085183 40.8747432725 38.2664726674 14.3724223507 22.7800282987 48.6714743926 60.8736775581 42.3559090343 20.7705507026 51.395894784 47.6305119192 65.3349384696 36.7881581459 26.8531772462 26.8901948078 53.7465104203 60.7559205762 12.159802723 29.118439017 38.785049252 15.9679192974 20.0151408824 7.1421857857 14.4383669693 55.7751481877 54.5843525778 243.2012280071 32.7417554418 121.8820495551 113.0966274398 202.4563591039 157.55244924 176.5936151446 246.2587427484 182.7623521443 28.9941623297 27.323707533 237.2877162027 205.6626133926 106.8475464403 77.2221768722 137.971043424 147.184494874 170.6452852727 204.6852962044 34.0623468603 147.2830870414 197.7656114571 134.0000639386 150.6940319735 141.6724918372 97.242603503 64.5397291672 175.1148890579 237.4903439325 181.1069234881 56.3672594331 191.9437945009 195.4548531401 245.3468732289 151.6167808767 90.7174341789 61.2903250104 214.4565894704 230.332065379 26.1876591147 117.8772374681 140.2984959534 42.1338852804 72.9620193005 41.8030640888 28.834629037 193.5098505597 212.2654814383 42.3864578121 10.9164056865 29.5858638973 18.9775469107 64.6273466431 28.5774748566 59.4792895283 48.5700169168 61.6749152584 30.9828597904 12.8928021837 57.0451623366 30.2084989342 44.7349534109 9.2001001004 42.898047339 21.7186550008 60.4717450849 40.9273564833 3.0875325618 50.0494079406 52.2393001994 48.550631631 24.8742155341 46.829372233 42.3835010374 19.8015193361 23.5462684343 61.4221766983 37.5362269903 21.9874749595 31.4839404065 60.3438589303 69.4208503825 53.8784282684 42.1931477006 11.0745478579 37.4258500715 42.0971656273 11.5566062437 48.5745380033 18.6404960472 33.4277935097 34.107161417 34.1489704248 3.2169086307 32.319226141 56.5421180077 2 4 3 4 3 4 2 2 1 3 4 1 1 1 2 3 4 1 3 3 1 3 1 4 2 2 1 2 4 3 3 4 1 3 1 3 4 3 4 4 3 3 2 3 3 1 3 2 41.2726973645 34.8990276356 -4.7262563805 54.543690645 25.1418800305 5.5906854084 1.7972804389 7.8111658831 5.2702676978 48.8282983171 31.1029124407 49.9678823126 29.5731596877 34.7823281304 30.371039156 36.3807024733 -1.5447413307 26.1312383633 62.4626067215 41.295541272 69.0222549528 5.8053396075 34.361262948 30.4367795438 35.682261541 43.9015596902 34.0722841953 23.6502999347 21.5889830129 22.3752040114 39.0239096466 54.0340533969 55.0926872699 39.8349896007 50.7813972158 20.8056501573 37.3915534457 9.7420310186 15.2421031134 8.0799356203 40.921047666 40.4475747451 5.2705179481 34.2592592121 57.8856684292 51.01574905 22.5690435276 67.8859570724 136.7201416153 100.2267433561 19.5214931943 202.9219135308 103.078142795 22.9776438362 29.8444850089 27.0604324558 20.9447029918 208.6492310249 174.272946715 231.6502894753 99.9660561696 150.8719190922 118.9453376119 134.9597183527 16.3622890265 96.5710608564 224.9892753139 143.2066312836 239.9355616991 29.3148217321 108.5310825756 113.6097288217 113.558680084 157.7441643126 123.2267002554 72.0743305291 120.055003013 84.8273232573 145.5904013709 206.0213565887 228.0133073371 165.6177784101 237.0212690193 46.2445259218 137.0568494462 53.9590507507 36.74062968 15.1573380033 181.5663087191 185.6429891244 49.3118915959 146.1289446778 208.5301231048 209.0512972151 91.1625325406 242.3911355993 21.8604184512 17.7259590035 28.1489272623 32.3781136808 40.3822717455 4.3635483286 33.6312324765 32.1289550935 25.3774813854 64.4512612921 27.166838008 57.7445633323 11.6361762716 28.6425693303 22.1893427363 43.5953691111 32.9799026314 16.6395082047 46.2221508612 28.4497016086 65.5404964976 9.2782134255 20.3900094293 19.7045803003 25.0615484743 30.9429563736 23.5236791503 12.1491017547 43.2173003744 39.2210359297 53.7547056873 36.6913882037 61.3864591929 22.7054725294 30.7622282877 11.9465079355 49.5458255648 39.9836492198 35.6257749024 33.6778137154 55.5174515463 50.0038485049 18.2694819444 60.4684056562 26.8836691094 26.137013701 49.1783567231 72.9969678652 1 3 1 1 2 1 1 3 1 3 4 2 2 3 3 2 4 4 4 2 4 3 2 4 2 4 1 1 3 2 3 4 2 4 2 3 4 2 4 4 4 1 1 1 2 2 1 1 60.1217087269 5.9099824869 9.9984362851 18.3070265916 13.8003498212 26.6579582935 51.7887141125 19.0043850785 16.0195306352 10.8991801689 15.2298194082 12.104640891 43.2937185479 7.5124424424 32.4163473496 24.833158753 1.6477155655 61.2730842193 62.2441530171 17.4262406333 17.0015440543 41.3350902046 38.3981693026 40.7973600122 24.468493804 39.7024178501 63.7077002424 3.8571729915 62.108959948 40.6191311261 18.1033699294 25.3203209537 15.7334650432 45.610444897 60.5821333064 46.9303533593 59.0936694748 49.2432282084 53.8496892535 39.9777742146 1.5154502684 17.4290468541 19.1684033989 19.4934780042 16.3009596323 60.8186261107 46.3240493648 30.1607617624 225.5489061261 42.5588410153 53.2350146573 57.1115771475 110.4362451948 161.2648789811 219.6065970117 69.4851435418 45.5346944207 17.0785246687 48.3816980692 73.1195293988 164.2515365115 10.3767714789 140.5534194862 100.3496801446 17.6154176503 217.8963765452 235.0402988763 141.9230210314 46.578071631 155.7585079693 207.5428037763 215.4485760131 91.4134692086 140.3373951092 229.7012195569 63.7708325359 236.7316184219 192.3685146308 70.1724387489 59.4914516143 43.3861064903 179.8670262153 208.3891622879 172.4882683593 236.4750923116 212.9800869444 234.1417912569 141.4218207241 25.0236816002 53.6586551524 69.6875077875 55.1815029603 48.6784046485 247.7860342992 206.75831174 128.0111307791 62.0468805989 31.0149096244 38.6838934566 9.3723655426 41.6442961109 26.3622982142 66.2888562796 42.4930661143 11.1333567293 1.6959734201 36.8553867052 34.5061362691 34.7323842899 30.5286844051 24.3287100558 20.1991371535 39.9168330737 27.1781800814 44.6318501815 44.1692947106 15.4756189641 30.4502400563 28.7519401441 58.6530061354 17.9338263874 48.8877046066 65.0699936943 13.831149801 41.0366305481 31.9651489984 36.0823471869 12.3926001263 14.5810869178 58.3392522456 53.5771443706 42.7774411137 59.8024206765 37.5816700358 41.3210653778 41.9780946407 9.0926640448 7.7412728316 39.0230940637 10.2433274957 36.3703380095 38.3546147428 35.5357545677 24.1923387325 4 1 4 2 1 3 4 3 4 2 2 2 3 3 4 4 2 2 2 2 3 1 1 3 2 1 3 3 3 2 4 3 3 1 2 2 3 1 3 2 2 4 2 4 1 3 3 3 -0.9929612359 12.1335818211 42.1907096035 56.365545453 9.8332778004 15.8083415952 28.6553025596 5.0697755261 14.6533893706 30.875463115 54.1719358595 11.0447298799 29.7426363328 31.3704404447 22.1411500022 22.0267764804 25.1414304722 21.8795309785 20.0966517861 10.079124276 33.3946466297 22.4928732274 55.6749055086 12.1199000916 61.4868796583 -6.9272570276 56.7058066612 42.3266787066 14.9326101022 39.3647575315 30.9556485257 45.8772010417 37.4016080177 32.0330297349 15.7737557472 41.1696412206 59.719242364 61.8954772993 50.9672301328 52.9152861308 39.9583438789 36.1792822352 49.4094882051 11.5723969625 28.7092760715 23.5351064169 23.2691013023 48.4365606008 41.4960972397 33.0595512005 215.1049987491 206.9277067934 37.6170447368 22.9444296616 151.3132269015 11.3449109479 88.1560328916 165.7605923944 231.7666512946 35.5235442935 95.4642819491 148.7246138444 85.9917263838 87.9533221521 117.3004547204 120.1609532205 81.7426724018 68.7264680891 140.1980411541 73.6709084122 214.5489663252 45.4094372471 238.8815554783 11.7614280266 204.4274941397 155.2786796707 95.0221995492 158.9171198312 143.4954541947 151.6923932476 145.7677249805 119.6649737851 69.9254715136 159.3985536394 205.6855723466 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