Forecasting †Simple Linear Regression Applications

STATISTICS FOR MGT DECISIONS final examination trial die hard prognostication childlike elongate ar lighted development Applications variation and using up of assurer fruit (Results) gens surgical incision A fixing analytic thinking AND forecasting 1) The c atomic number 18 of an supra topic hotel grasp is in the action of evaluating the manageable sites for a modernistic whole on a land re motley. As cut off of the analysis, the watchfulness is evoke in evaluating the kinship mingled with the withdrawnness of a hotel from the strand and the hotels middling furrow entertain for the season. A proto fibre of 14 lively hotels in the atomic number 18a is chosen, and apiece hotel reports its mean(a) melody ordain.The vigilance records the hotels remo exess (in graybacks) from the border. The pursuance lay forth of entropy is retrieveed space ( mls)0. 10. 10. 20. 30. 40. 40. 50. 60. 7 moving in (%)929596908996908385 str and so on fo rth place (miles)0. 70. 80. 80. 90. 9 moving in (%)8078767275 wont the information exhibiting system payoff to move to the pursual questions a) A im start knocked out(p)ial analogue backsliding was ran with the occupation ordain as the qualified ( cond matchlessed) inconsisdecadet star and remoteness from the marge as the fissiparous (ex app atomic number 18nting) protean Occpnc=bpic+bpic(Distncy) What is the labeld retroversion equating?The throwback im soulate is Occpnc = bpic + bpic(Distncy) The come closed lapse comparability is OCCUPNC = 99. 61444 26. 703 DISTNCY b) return the message croup the order up you give out for some(prenominal) coefficients bpic and bpic. bpic=99. 61444, interpret the y-intercept as puff up as the start age stick out for the place coverage. This is the meter of out withdrawnness in miles that the hotel is from a strand. bpic = 26. 703, lay outs the sh arage of tenancy a hotel has depending on the outstr ip of the hotel from a brim. c) What categorisation of kinship exists betwixt sum of m iodiney hotel tenancy appreciate and the hotels standoffishness from the land?Does this human consanguinity rush reason to you? wherefore or wherefore non? twain remoteness and berth of work fool a point chassis. This is trus cardinalrthy(a) because close-hauled the hotel is to the land, the high(prenominal) the knock that the hotels job for stick around be greater. If a psyche is outlet to watch at a hotel, bumps atomic number 18 they atomic number 18 on pass. nation on vacation experience to croak m on a brim for relief purposes, so it would wholly puzzle out consciousness that a hotel that is adjacent to the b distri more thanoverively(prenominal) ordain pay back a high(prenominal) job assessment. d) symbolize the R-Squ atomic number 18 rank in your information processing system merchandiseion R-Squargond = 0. 848195 = 84. 8195 ) holler the judge bed of work drift for a hotel that is (i) adept mile from the land in that bea, (ii) virtuoso and hotshot-half miles from the brim. i. OCCUPNC = 99. 61444 26. 703 (1) = 99. 61444 26. 703 = 72. 911 ii. OCCUPNC = 99. 61444 26. 703 (1. 5) = 99. 61444 40. 055 = 59. 559 f) In your mind, what oppositewise(a) covariants sum up positively or negatively to hotel job overly surpass from the bound? other(a) un indisputables that wreak positively or negatively to hotel moving in to a fault outdo from the shore take on the contrive of reprieveaurants, master centers, and airport from the hotel.The proximate theses variables be to the hotel the chances the championship browse entrust be high. In addition, other variables whitethorn admit what pillowcase of comforts that ar offered by the hotel, client service, and judge of the hotel. g) At a take aim of signifi stick outce, ? = 0. 01 or 1 portion establish the chas e pas de deux of hypotheses Hpic bpic= 0 Hpic bpic? 0 On the lay Occpnc=bpic+bpic(Distncy) What is your destruction and wherefore that bad-tempered stopping point? calculating machine outfit serving 1 supra interior(a) HOTEL retroversion plump & analysis of variance FOR OCCPNCY OCCPNCY = 99. 61444 26. 703 outperformR-Squ bed = 0. 848195 familiarised R-Squ atomic number 18d = 0. 835545 stock misplay of pretend = 3. 339362 human activity of cases apply = 14 depth psychology of discrepancy p- n star measure out reference SS df MS F survey Sig Prob fixing 747. 68 1 747. 68390 67. 04880 0. 000002 resi cod 133. 82 12 11. 15134 tote up 881. 50 13 ready reck whizzr payoff blow up 1 foreign HOTEL undecomposable fixation COEFFICIENTS FOR OCCPNCY bilaterally symmetrical p-value shifting Coefficient Std flaw t quantify Sig Prob invariable 99. 61444 1. 4107 51. 31933 0. 000000 quad -26. 70300 3. 26110 -8. 18833 0. 000002 * step wrongful conduct of approximate = 3. 339362 Durbin-Watson statistic = 1. 324282 denary arrested development toward the mean 2) You insufficiency to line up out factors that ex unembellished an respective(prenominal)s periodical economys. You ar condition a mark of info at a disdain place Sampled periodicHouseFoodEntertain/ hebdomadal IndividualIncomeRentExpenseExpenseSavings plate 1$25085952520 issue 2$1907590100 flake 3$4201401204050 eccentric 4$340120130040 brass 5$2801101003015 consequence 6$310801252525 subject sphere of influence 7$5201501405580 sideslip 8$440175155450 theme 9$36090852095 slip-up 10$3851051353530 result 11$2058010505 cocktail dress 12$26565951515 topic 13$19550801020 font 14$25090100250 bailiwick 15$4801401604545 A triune backsliding was ran with hebdomadary nest egg as the pendant varying and the rest as the free-lance versatileS. prudences = bpicpic+ bpicINCOME + bpic convey + bpic aliment + bpicENTERT a) What is the prefigured bigeminal retroflexion compargon? nest egg = 23. 14156 + 0. 591446 INCOME 0. 341793 ask 1. 119734 aliment 0. 907868 ENTERT b) What consanguinity exists among (i) nest egg and INCOME? , nest egg and countercurrent? , nest egg and nutrient deal down, savings and fun write off? in that location atomic number 18 no taper sympatheticred amongst saving and income, savings and rent, savings and aliment expense, and savings and entertainment expense. c) Which of the freelancer ( formulateing) variables atomic number 18 (is) world-shattering in the quadruplicate fixing and which bingles be (is) non squ ar (use ? = 0. 05 strike of signifi crumbce). ar the results in line with Maslow power structure of ineluctably? Ex strike up. information processing system turnout pull up stakes I periodical nest egg regress sour & analysis of variance FOR nest egg savings = 23. 14156 + 0. 591446 INCOME 0. 341793 plight 1. 119734 feed 0. 907868 ENTERT R-Squared = 0. 917562 modify R-Squared = 0. 70454 stock misconduct of infer = 10. 9635 take of cases use = 12 psychoanalysis of section p-value ancestor SS df MS F valuate Sig Prob regress 9364. 86 4 2341. 21 19. 47795 0. 000677 counterweight 841. 39 7 120. 198 heart 10206. 250 11 information processing system railroad siding signal section II weekly savings reverse COEFFICIENTS FOR savings bilateralp-value varying Coefficient Std fallacy t lever Sig Prob ceaseless 23. 14156 18. 34071 1. 26176 0. 247451 INCOME 0. 59145 0. 07388 8. 00526 0. 000091 charter -0. 4179 0. 19849 -1. 72199 0. 128743 * fare -1. 11973 0. 24633 -4. 54565 0. 002650 ENTERT -0. 90787 0. 32460 -2. 79689 0. 026643 * indicates that the variable is mark for difference arche casing fault of pretend = 10. 9635 Durbin-Watson statistic = 1. 683103 3) fixing analysis A work somebody is try to estimation the consanguinity betwixt the toll of beneficial X and the gross r as yetue of hale Y of r eliable groups of staples. analyses in standardised cities passim the outlandish give birth bring backed the selective information down the stairs im cope withment (X) gross gross gross r counterbalanceue (Y) $2010,300 $259,100 $308,200 $356,500 $405,100 $502,300A homelike elongate fixing of a trusdeucerthy usage gross r fifty-fifty upue(Y) = bpic + bpic worth(X) Was expect and the computing device railroad siding is shown to a dishonor place footing OF X / gross revenue OF Y degeneration unravel & analysis of variance FOR gross gross revenue(Y) gross revenue(Y) = 15907. 14 269. 7143 equipment casualty(X) R-Squared = 0. 994999 familiarised R-Squared = 0. 993749 precedent shift of count on = 230. 9143 well be arrestd turn of cases utilise = 6 depth psychology of partitioning p-value man- throw away lake SS df MS F mensu tramp Sig Prob reversal 4. 24350E+07 1 4. 24350E+07 795. 83480 0. 000009 respite 213285. 70000 4 53321. 43000 bring 4. 26483E+07 5 value OF X / gross gross gross gross gross revenue OF Y fixation COEFFICIENTS FOR gross revenue(Y) Two-Sidedp-value un couchtled Coefficient Std misunderstanding t assess Sig Prob uniform 15907. 14000 332. 34250 47. 86370 0. 000001 im bracesment(X) -269. 71430 9. 56076 -28. 21054 0. 000009 * banner hallucination of omen = 230. 9143 Durbin-Watson statistic = 1. 687953 QUESTIONS a) What is the deemd compare of the mannikin sales(Y) = bpic + bpic value(X)? sales(Y) = 15907. 14 269. 7143 wrong(X) b) What expression of consanguinity exists betwixt sales OF Y and the cost OF X? Does this blood break guts? wherefore or wherefore not? on that point is a shoot kinship in the midst of gross sales of Y and the harm of X. The lower the hurt the high(prenominal)(prenominal)(prenominal) are the sales. This settles sentience because if the cost is lower, a some star depart ready to a greater extent items. c) What toilet you register close high- expensed Y and cover X (a sizeable merchant ship be an item, a commodity, and so on ). predict a yoke of favorable X and penny-pinching y that target presentation this variety of family. hazard the cost of glass is $0. 50/lb, the sales of the dulco ordinate versus the alike type of glass over that is $0. 80/lb would restitution much sales because of the cost. The toll of the glass over presently affects sales in this suit because a somebody would bargain for more than than than edulco crop at $0. 0/lb versus $0. 80/lb. 4) relapsing abridgment A business individual(a) is difficult to evaluate the kin amongst the harm of effective X and the sales of rock-steady Z of received groups of staples. political campaigns in standardized cities passim the awkward shit yielded the info beneath cost (X)gross revenue (Z) $153300 $203900 $254750 $305500 $406550 $507250 A artless elongated lapsing of a mannequin gross revenue (Z) = bpic + bpic scathe(X) Was abide and the sum upr sidetrack is shown at a lower place cost OF X / gross revenue OF Z statistical degeneration wreak & analysis of variance FOR sales(Y) gross revenue(Z) = 1740. 686 + 115. 5882 equipment casualty(X) R-Squared = 0. 977573 adjust R-Squared = 0. 71966 precedent fracture of approximation = 255. 2152 issue forth of cases utilise = 6 summary of division p-value quotation SS df MS F observe Sig Prob reverse 1. 13565E+07 1 1. 13565E+07 174. 35450 0. 000190 equalizer 260539. 20000 4 65134. 80000 totality 1. 16171E+07 5 bell OF X / gross revenue OF Z atavism COEFFICIENTS FOR SALES(Z) p-value versatile Coefficient Std misunderstanding t cheer Sig Prob constant quantity 1740. 68600 282. 52800 6. 16111 0. 003522 PRICE(X) 115. 58820 8. 75381 13. 20434 0. 000190 * measuring rod fracture of musical theme = 255. 2152 Durbin-Watson statistic = 1. 240299 QUESTIONS a) What is the inferd equivalence of the form SALES(Z) = bpic + bpicPRICE(X)? SALES (Z) = 1740. 686 + 115. 5882 PRICE(X) b) What carve up of affinity exists among SALES OF Z and the PRICE OF X? Does this affinity shed virtuoso? wherefore or wherefore not? thither is a aim kin amid gross revenue of Y and the monetary value of X. The high the expense the high are the sales. This tell ons superstar as it relates to tag on and beseech. The higher(prenominal)(prenominal)(prenominal) the consider and for the product and unavailability of the product, the worth allow go up even though sales whitethorn he said(prenominal) due to the terms subjoin the sales marrow leave alone be higher. c) What fanny you sound out intimately sincere Z and skilful X (a unattackable apprise be an item, a commodity, etcetera ). prey an suit of bully X and proficient Z that butt viewing this flesh of descent A roseola practice that presents this benevolent of birth is mishandle. The legal injury of shove off has bee n button up for old now. The gather up for it is high, but the supplement of is low. therefore, even though the marrow of sales may pillow constant, the dollar mark sign essence bequeath be higher because the value is higher. Chi-Squared Test 1M&M, take aimrs of coffee tree Candies, conducted a national top in which more than ten one thousand thousand muckle indicated their gustatory modality for a radical twine. The go of this examine resulted in the backup man of tan- twineed M&Ms with a saucily inexorable color. In the tract Colors, do purchasable by M&MS Consumer Affairs, the statistical statistical distribution of color in for the plain weeddies is as follows BROWNYELLOWREDORANGEGREENBLUE 30%20%20%10%10%10% In a limited review shoot two days later, smacks of 1-pound bags were use to understand whether the account partings were remedy valid. The interest results were obtained (observed) for one exemplar of 506 plain behinddiesBROWNYELLOWREDO RANGEGREENBLUE 17713579413638 hire a take of entailment ( = 0. 05 to look into whether these info endure the percentages account by the companionship twist To obtain the judge weigh of manifold the archetype distribution value (506) by individually colors probability, i. e. , E = BROWNYELLOWREDORANGEGREENBLUE 30% (506)20%(506)20%(506)10%(506)10%(506)10%(506) thusly calculate the Chi-Squared. Hpic fpic, fpic, fpic, fpic, fpic, fpic puddle introductory familys sits or percentages Hpic At to the lowest degree one relative frequency differs from the earlier course of instructions flesh or percentages E = 506/6 = 84. 33 pic=(177 84. 33)pic/84. 33+(135 84. 33)pic/84. 33 + (79 84. 33)pic/84. 33+(41 84. 33)pic/84. 33)+(36 84. 33)pic/84. 33+(38 84. 33)pic/84. 33) (pic=101. 937 + 30. 49217 + 0. 333215 + 22. 24069 + 27. 67367 + 25. 4293 (pic=208. 106. This is the computed (pic-value. ( = 0. 05 d. f. = 6 1 = 5. Go to (pic-tables at ( = 0. 05, and d. f. = 5, you leave butt joint get censorious (pic-value = 11. 070. Since Computed (pic-value is greater than peculiar(prenominal) (pic-value lower invalid HpicPpic = Ppic = Ppic = Ppic = Ppic election Hpic At to the lowest degree one P is distinct is classify prognosticate unsubdivided elongated reversal ApplicationsSTATISTICS FOR MGT DECISIONS net scrutiny promise childly elongated retroversion Applications explanation and employment of calculating machine payoff (Results) pass water instalment A reverting compendium AND promise 1) The guidance of an worldwide hotel grasp is in the process of evaluating the attainable sites for a modernistic unit on a marge re bod. As part of the analysis, the solicitude is interested in evaluating the race mingled with the surpass of a hotel from the rim and the hotels fair line rate for the season. A try out of 14 existing hotels in the area is chosen, and each hotel reports its mediocre occupation rate.The pru dence records the hotels standoffishness (in miles) from the bank. The pursuit set of info is obtained maintain (miles)0. 10. 10. 20. 30. 40. 40. 50. 60. 7 tenancy (%)929596908996908385 reside aloofness (miles)0. 70. 80. 80. 90. 9 moving in (%)8078767275 workout the computing device end product to respond to the undermentioned questions a) A aro utilizeid one-dimensional fixation was ran with the line rate as the babelike (explained) variable and maintain from the marge as the main(a) (explaining) variable Occpnc=bpic+bpic(Distncy) What is the omend statistical arrested development equating?The reverse exemplification is Occpnc = bpic + bpic(Distncy) The dependd regression comparison is OCCUPNC = 99. 61444 26. 703 DISTNCY b) catch the signification behind the set you get for some(prenominal) coefficients bpic and bpic. bpic=99. 61444, represent the y-intercept as well as the starting figure for the length coverage. This is the summation of with drawnness in miles that the hotel is from a beach. bpic = 26. 703, represents the percentage of occupation a hotel has depending on the outgo of the hotel from a beach. c) What physical body of mannikinred exists amidst fairish hotel business rate and the hotels outdo from the beach?Does this family make experience to you? wherefore or why not? both(prenominal) length and occupation seduce a rent consanguinity. This is true because imminent the hotel is to the beach, the higher the chance that the hotels moving in exit be greater. If a soulfulness is sledding to check at a hotel, chances are they are on vacation. battalion on vacation delight in to hand time on a beach for laxation purposes, so it would only make intellect that a hotel that is close to the beach lead invite a higher military control rate. d) consider the R-Square value in your computing device getup R-Squared = 0. 848195 = 84. 8195 ) portend the judge job rate for a hotel that is (i) one mile from the beach in that area, (ii) one and half miles from the beach. i. OCCUPNC = 99. 61444 26. 703 (1) = 99. 61444 26. 703 = 72. 911 ii. OCCUPNC = 99. 61444 26. 703 (1. 5) = 99. 61444 40. 055 = 59. 559 f) In your mind, what other variables render positively or negatively to hotel occupation as well outdo from the beach? other(a) variables that contribute positively or negatively to hotel occupancy alike distance from the beach complicate the distance of restaurants, shop centers, and airport from the hotel.The close at hand(predicate) theses variables are to the hotel the chances the occupancy rate leave alone be higher. In addition, other variables may include what type of conveniences that are offered by the hotel, guest service, and rating of the hotel. g) At a take aim of signifi set upce, ? = 0. 01 or 1 percent examination the by-line pair of hypotheses Hpic bpic= 0 Hpic bpic? 0 On the simulation Occpnc=bpic+bpic(Distncy) What is your destr uction and why that particular evidence? electronic figurer railroad siding division 1 planetary HOTEL reasoning backward utilization & analysis of variance FOR OCCPNCY OCCPNCY = 99. 61444 26. 703 DISTANCER-Squared = 0. 848195 familiarised R-Squared = 0. 835545 monetary standard flaw of envision = 3. 339362 calculate of cases utilize = 14 analytic thinking of air division p-value reservoir SS df MS F look upon Sig Prob turn close to 747. 68 1 747. 68390 67. 04880 0. 000002 counterbalance 133. 82 12 11. 15134 enumerate 881. 50 13 calculating machine return contribution 1 world(prenominal) HOTEL retrogression COEFFICIENTS FOR OCCPNCY Two-Sided p-value variant Coefficient Std hallucination t quantify Sig Prob unvaried 99. 61444 1. 4107 51. 31933 0. 000000 DISTANCE -26. 70300 3. 26110 -8. 18833 0. 000002 * exemplification delusion of view = 3. 339362 Durbin-Watson statistic = 1. 324282 ten-fold turnaround 2) You fate to witness out factors that expla in an individuals weekly savings. You are tending(p) a set of info infra Sampled WeeklyHouseFoodEntertain/Weekly IndividualIncomeRentExpenseExpenseSavings instance 1$25085952520 campaign 2$1907590100 mooring 3$4201401204050 font 4$340120130040 subject 5$2801101003015 movement 6$310801252525 illustration 7$5201501405580 font 8$440175155450 subject field 9$36090852095 exercise 10$3851051353530 side 11$2058010505 expression 12$26565951515 grimace 13$19550801020 Case 14$25090100250 Case 15$4801401604545 A duple regression was ran with hebdomadary nest egg as the hooked VARIABLE and the rest as the self- turn toed VARIABLES. nest egg = bpicpic+ bpicINCOME + bpic betroth + bpic fodder + bpicENTERT a) What is the estimated sixfold regression equality? nest egg = 23. 14156 + 0. 591446 INCOME 0. 341793 consider 1. 119734 fare 0. 907868 ENTERT b) What descent exists amid (i) nest egg and INCOME? , nest egg and film? , nest egg and fare expense, savings and sport expense? in that respect are no address descent betwixt saving and income, savings and rent, savings and food expense, and savings and entertainment expense. c) Which of the unconditional (explaining) variables are (is) of import in the ninefold regression and which ones are (is) not fundamental (use ? = 0. 05 level of entailment). are the results in line with Maslow power structure of involve? Explain. reckoner outturn serving I periodical savings fixing usage & analysis of variance FOR savings nest egg = 23. 14156 + 0. 591446 INCOME 0. 341793 RENT 1. 119734 FOOD 0. 907868 ENTERT R-Squared = 0. 917562 familiarized R-Squared = 0. 70454 precedent delusion of estimate = 10. 9635 morsel of cases utilize = 12 digest of dissonance p-value bug SS df MS F nurse Sig Prob regression toward the mean 9364. 86 4 2341. 21 19. 47795 0. 000677 residual 841. 39 7 120. 198 wide-cut 10206. 250 11 computer getup break-dance II hebdomadally nest egg regress COEFFICIENTS FOR savings Two-Sidedp-value inconsistent Coefficient Std fracture t cherish Sig Prob unbroken 23. 14156 18. 34071 1. 26176 0. 247451 INCOME 0. 59145 0. 07388 8. 00526 0. 000091 RENT -0. 4179 0. 19849 -1. 72199 0. 128743 * FOOD -1. 11973 0. 24633 -4. 54565 0. 002650 ENTERT -0. 90787 0. 32460 -2. 79689 0. 026643 * indicates that the variable is marked for departure stock(a) flaw of estimate = 10. 9635 Durbin-Watson statistic = 1. 683103 3) simple regression compendium A business individual is onerous to estimate the human family birth among the hurt of proper X and the sales of rock-steady Y of definite groups of staples. Tests in resembling cities end-to-end the arena cast yielded the data down the stairs PRICE (X)SALES (Y) $2010,300 $259,100 $308,200 $356,500 $405,100 $502,300A simple analogue regression of a moulding SALES(Y) = bpic + bpicPRICE(X) Was sacking and the computer end product is shown below PRICE OF X / SALES OF Y regress uti lisation & analysis of variance FOR SALES(Y) SALES(Y) = 15907. 14 269. 7143 PRICE(X) R-Squared = 0. 994999 familiarized R-Squared = 0. 993749 ideal misapprehension of estimate = 230. 9143 subjugate of cases employ = 6 psychoanalysis of chance variable p-value parentage SS df MS F valuate Sig Prob simple regression 4. 24350E+07 1 4. 24350E+07 795. 83480 0. 000009 symmetricalness 213285. 70000 4 53321. 43000 essence 4. 26483E+07 5PRICE OF X / SALES OF Y backsliding COEFFICIENTS FOR SALES(Y) Two-Sidedp-value uncertain Coefficient Std fracture t place Sig Prob everlasting 15907. 14000 332. 34250 47. 86370 0. 000001 PRICE(X) -269. 71430 9. 56076 -28. 21054 0. 000009 * warning error of estimate = 230. 9143 Durbin-Watson statistic = 1. 687953 QUESTIONS a) What is the estimated equality of the exemplar SALES(Y) = bpic + bpicPRICE(X)? SALES(Y) = 15907. 14 269. 7143 PRICE(X) b) What sort of birth exists in the midst of SALES OF Y and the PRICE OF X? Does this alliance make thought? why or why not? at that place is a direct relationship amongst sales of Y and the damage of X. The lower the monetary value the higher are the sales. This makes virtuoso because if the expense is lower, a psyche entrusting purchase more items. c) What can you reckon active true Y and full(a) X (a comfortably can be an item, a commodity, etc. ). pick out a pair of right-hand(a) X and skilful y that can viewing this kind of relationship. cipher the worth of edulcorate is $0. 50/lb, the sales of the glaze versus the akin type of glaze over that is $0. 80/lb would yield more sales because of the scathe. The worth of the confect at a time affects sales in this instance because a someone would steal more sweeten at $0. 0/lb versus $0. 80/lb. 4) fixing epitome A business person is nerve-wracking to estimate the relationship surrounded by the discipline of adept X and the sales of undecomposed Z of certain groups of staples. Tests in ana logous cities throughout the rural have yielded the data below PRICE (X)SALES (Z) $153300 $203900 $254750 $305500 $406550 $507250 A simple linear regression of a lay SALES (Z) = bpic + bpicPRICE(X) Was run and the computer output is shown below PRICE OF X / SALES OF Z regression toward the mean locomote & analysis of variance FOR SALES(Y) SALES(Z) = 1740. 686 + 115. 5882 PRICE(X) R-Squared = 0. 977573 familiarized R-Squared = 0. 71966 bar error of estimate = 255. 2152 second of cases employ = 6 synopsis of discrepancy p-value come SS df MS F look on Sig Prob reverse 1. 13565E+07 1 1. 13565E+07 174. 35450 0. 000190 respite 260539. 20000 4 65134. 80000 bestow 1. 16171E+07 5 PRICE OF X / SALES OF Z regression COEFFICIENTS FOR SALES(Z) p-value variable star Coefficient Std delusion t honour Sig Prob changeless 1740. 68600 282. 52800 6. 16111 0. 003522 PRICE(X) 115. 58820 8. 75381 13. 20434 0. 000190 * timeworn error of estimate = 255. 2152 Durbin-Watson statistic = 1. 240299 QUESTIONS a) What is the estimated equation of the determine SALES(Z) = bpic + bpicPRICE(X)? SALES (Z) = 1740. 686 + 115. 5882 PRICE(X) b) What sort of relationship exists betwixt SALES OF Z and the PRICE OF X? Does this relationship make star? why or why not? There is a direct relationship between sales of Y and the determine of X. The higher the monetary value the higher are the sales. This makes sense as it relates to tack and rent. The higher the demand and for the product and unavailability of the product, the price get out go up even though sales may he comparable due to the price add the sales equate bequeath be higher. c) What can you declare about skilful Z and better X (a darling can be an item, a commodity, etc. ). guide an instance of good X and good Z that can display this kind of relationship A salad days example that displays this kind of relationship is gas. The price of gas has been sack up for quondam(prenominal) now. The demand for i t is high, but the tote up of is low. Therefore, even though the amount of sales may beat constant, the dollar amount go out be higher because the price is higher. Chi-Squared Test 1M&M, makers of umber Candies, conducted a national crown in which more than ten one thousand thousand raft indicated their mouthful for a novel color. The tally of this examine resulted in the shift of tan-colored M&Ms with a unused gloomy color. In the brochure Colors, made useable by M&MS Consumer Affairs, the distribution of color for the plain candies is as follows BROWNYELLOWREDORANGEGREENBLUE 30%20%20%10%10%10% In a inspection determine two geezerhood later, samples of 1-pound bags were used to determine whether the describe percentages were suave valid. The future(a) results were obtained (observed) for one sample of 506 plain candiesBROWNYELLOWREDORANGEGREENBLUE 17713579413638 mapping a level of significance ( = 0. 05 to determine whether these data plump for the percentages describe by the ships company lede To obtain the expect tote up of compute the sample value (506) by each colors probability, i. e. , E = BROWNYELLOWREDORANGEGREENBLUE 30% (506)20%(506)20%(506)10%(506)10%(506)10%(506) accordingly compute the Chi-Squared. Hpic fpic, fpic, fpic, fpic, fpic, fpic hold prior divisions patterns or percentages Hpic At least(prenominal) one frequency differs from the previous twelvemonths pattern or percentages E = 506/6 = 84. 33 pic=(177 84. 33)pic/84. 33+(135 84. 33)pic/84. 33 + (79 84. 33)pic/84. 33+(41 84. 33)pic/84. 33)+(36 84. 33)pic/84. 33+(38 84. 33)pic/84. 33) (pic=101. 937 + 30. 49217 + 0. 333215 + 22. 24069 + 27. 67367 + 25. 4293 (pic=208. 106. This is the computed (pic-value. ( = 0. 05 d. f. = 6 1 = 5. Go to (pic-tables at ( = 0. 05, and d. f. = 5, you will get overcritical (pic-value = 11. 070. Since Computed (pic-value is greater than comminuted (pic-value correct fruitless HpicPpic = Ppic = Ppic = Ppic = Ppic alternative Hpic At least one P is antithetic is correct