Week 6 module notes - i A. Interpret Simple Regression...

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Unformatted text preview: i A. Interpret Simple Regression Dutput— lnterrelations Among Elements of the F E? Avery broad consensus has emerged around the proposition that global warming is a realitywith likely serious global consequences. lvlany energy economists and political leaders are advocating a I: = 0.335 multiprohged approach to providing alternative energy, including nuclear, natural gas. clean coal, and renewable sources from Standard Error = [WEE geothermal, solar and wind energyforms. Municipalities and states have been asked by the Department of RM“ Vflurflflfl' “Ewe” mmmadammfl' “3595' Energyto assess their energy requirements for each ofthe alternative fuels. In particular, they have decided to focus initially on F : “'39 natural gas. given the enormity ofUE. reserves and its relative cleanliness. Round the F value totwodecimal places. Attached is a portion of the regression outputfor selected municipalities in Illinois for “ID reporting periods {weeks}. The dependehtvariahle is consumption ofnatural gas in millions ofcuhic feet [FUEIEUFIS} and the independentvariahle is the temperature ['l'emp}, measured in degrees Fahrenheit. Determine R squared, the Standard Error. and F. El Simple LinearRegressionAnalysis Alklsx Regression Analysis F n 1U r 41.915 it 1 Std- Errer Dep- 1ii'er. FuelCens AND‘JA table .................... F is fire 33 regressienfdi' Standard regression Errer is ever 33 r“? is the Hesidueir’n-E residue-Huff regressien :52 find the sqn‘ residuei H fete-i in! E? Ayery broad consensus has emerged around the proposition that global warming is a reality, with liker serious global conseguences. luloreoyer, while there is still not unanimity that global warming is entirely man-made, there is broad agreement that it is desirable to cut emissions from coal and petroleum. Finally, many energy economists and political leaders are adyocating a multipronged approach to proyiding alternatiye energy including nuclear, natural gas, clean coal, and renewable sources from solar and wind. Municipalities and states haye been aslced by the Depaitment of Energy to assess their energy requirements for each ofthe alternatiye fuels. In particular, they haye decided to focus initially on natural gas, giyen the enormity ofLJE. reseryes and its relatiye cleanliness. The regression outputfor selected municipalities in Illinois for 1 El reporting periods (weeks) is attached below. The dependent yariable is consumption ofnatural gas in millions ofcubic feet (Fuelcons) and the independentyariable is the temperature (Temp), measured in degrees Fahrenheit. Write the regression equation, and explain the regression coefficients. Simple LinearRegression Analysis EIl-ElBJtlsx l lu'llelcorrie. l-tmlr ea iIr'Sli Tue Feb 8 2i E:-:er cise 'I regression equation: y: + it Enter your answers to four decimal places. interpretation of b; : It. This tells us the ayerage temperature forthe selected municipalities in Illinois during the testing period. B. This tells us the ayerage amount ofnatural gas consumed during thetesting period. C. This says we are 95% confident that in the population each additional degree {Fahrenheit}: ofincrease in temperature will result in a decrease offuel consumption around this yalue. D. This tells us how much natural gas is estimated to be consumed when the temperature = III. E. This yalue has no practical interpretation. interpretation of b- : i-t. This tells us thatfor each additional degree (Fahrenheit) of u E? Ayery broad consensus has emerged around the proposition that global warming is a reality, with liker serious global conseguences. luloreoyer, while there is still not unanimitythat global warming is entirely man-made, there is broad agreement that it is desirable to cut emissions from coal and petroleum. Finally, many energy economists and political leaders are adyocating a multipronged approach to proyiding alternatiye energy including nuclear, natural gas, clean coal, and renewable sources from solar and wind. Municipalities and states haye been asked by the Department of Energy to assess their energy requirements for each ofthe alternatiye fuels. In particular, they haye decided to focus initially on natural gas, giyen the enormity ofLJE. reseryes and its relatiye cleanliness. The regression outputfor selected municipalities in Illinois for 1 III reporting periods {weeks}: is attached below. The dependent yariable is consumption ofnatural gas in millions ofcubic feet (Fuelcons) and the independent yariable is the temperature (Temp), measured in degrees Fahrenheit. Write the regression eguation, and explain the regression coefficients. Simple LinearRegression Analysis EI1-EIBxlsx I Welcome. Andi ea {PS Tue Feb 81 Exel cise IE TI interpretation of b- : it. This tells us that for each additional degree (Fahrenheit) of increase in temperature, we can expect an increase of.11T3 millions ofcubic feet of natural gas. B. This tells us that at a temperature of1 degree (Fahrenheit), one can expect that there will be 15.2559 millions ofcubic feet ofnatural gas used. 12. This is the estimate for natural gas used when the temperature = D. D. This tells us that for an each additional degree (Fahrenheit) of increase in temperature, we can expect a decrease of.11T3 millions ofcubic feet ofnatural gas. E. This yalue has no practical interpretation. I I Welcome. Katie Ed: 7 E. Interpret Simple Linear Regression Output — Descripticn and Point Estimates Wed Feb 52: ll-l E? E Exercise: Municipalities and states haye been asked hythe Departmenth Energy to assess their energy requirements for each dfthe Standard Errcr : [er135 alternatiye fuels. In particular, they have decided td fdcus initially dn natural gas, giyen the endrmity del.5. resenies and its relatiye Round yourflnalanswertctllreedecimal places. cleanliness. Here is the ayailahle data: FRIED“ Temp Interpretatidn dfthe Standard Errdr: 12.5 25.0 11 T 23 D A. This tells us how much the fuel cdnsumptidn Will increase for ' ' each drdp in temperature df1 degree Fahrenheit. 11.1 215 1.12 310 E. This tells us the mean fuel cdnsumptidn we shduld expectfdr any giyentemperature. 12.4 32.5 1:13 33g C. This tells us how much the UbSEWEd fuel cdnsumptidn yalues 9-4 453 yaryfrdm the predicted yalues. 5.5 515 D. This tells us hdw much we shduld expectthe temperature td drdp an 531 fdr each increase in fuel consumption df.T55 millidns cf cuhicfeet cf natural gas. .T".5 52.5 The regressidn dutputfdr selected municipalities in |||indis fdr1IZI '5' THE value “33 “0 practical importance- repdrting peridds Weeks} is attached heldw. The dependent yariahle is cdnsumptidn dfnatural gas in millidns dfcuhicfeet 2|: [Fuelcdns} and the independentyariahle is the temperature [‘femp}, measured in degrees Fahrenheit. WelcomeI Katie Son 7 B. Interpret Simple Linear Regression Dutput— Description and Point Estimates Wed Feb 32: " Exercisef A very broad consensus has emerged around the proposition that global warming is a reality, with likely serious global consequences. Moreover, while there is still not unanimity that global warming is Round your final answer to three decimal places. entirely man—made. there is broad agreement that it is desirable to cut emissions from coal and petroleum. Finally, many energy economists and political leaders are advocating a multipronged approach to providing alternative energy including nuclear, natural gas, clean coal, and renewable sources from solar and wind. Coefficientofdetermination = 0.835 Interpretation ofthe coefficient ofdetermination: A. This is the proportion ofthe total variation in temperature (in degrees Fahrenheit} that is explained by the simple linear regression model. Municipalities and states have been asked by the Department of Energy to assess their energy requirements for each ofthe alternative fuels. In particular, they have decided to focus initially on natural gas, given the enormity ofLJB. reserves and its relative cleanliness. E. This is the point estimate ofthe change in fuel consumption [in millions of cubicfeet} associated with each degree {Fahrenheit} increase in temperature. C. This is a measure ofthe variability ofthe observed values offuel The regression output for selected municipalities in Illinois for till Cflngumptm” mm the” madman ugh-'95 at pammartemperatureg' reporting periods {weeks} is attached below. The dependent variable is consumption ofnatural gas in millions of cubicfeet (Fuelcons} and the independent variable is the temperature {Temp}, measured in degrees Fahrenheit. D. This is the proportion ofthe totalvariation infuel consumption that is explained by the simple linear regression model. E. This value has no practical interpretation. W Correlation coefficient = 43.915 51 i Simple LinearRemeggmnpnawgig 31-33:le Roundyourfinal answertotllree decimal places. Using the following lvlegaStat output, identify the coefficient of determination and the correlation coefficient. and interpret each of them. WelcomeI Katie El: 7 E. Interpret Simple Linear Regression Dutput — Description and Point Estimates Wed Feb s; " Exercise Iii A yery broad consensus has emerged around the proposition that corralatmn memmem _ global warming is a reality, with lilter serious global consequences. ROI!“ Hflflffiflfll BHEWEHD “"99 GECimfll NECES- lyloreoyer, while there is still not unanimity that global warming is entirely man—made. there is broad agreement that it is desirable to Interpretatmn Ufthe mnelatim: cut emissions from coal and petroleum. Finally, many energy economists and political leaders are adyocating a multipronged A. This tells us thatthere is a strong negatiye relationship between approach to proyiding alternatiye energy including nuclear, natural fuel consumption and temperature. gas, clean coal, and renewable sources from solar and wind. E. This is the point estimate ofthe change in fuel consumption Municipalities and states haye been aslted by the Department of associated with each degree increase in temperature. Energy to assess their energy requirements for each ofthe alternatiye fuels. In particular, they hate decided to focus initially on C. Because ofthe negatiye yalue, this tells us to drop the natural gas. giyen the enormity ofUS. reseryes and its relatiye E temperature yariable and IDDHfo otherways to explain what driyes cleanliness. fuel consumption. The regression output for selected municipalities in Illinois for till D. This tells us the proportion ofthe total yariation in the till fuel reporting periods {weeks} is attached below. The dependent consumption yalues that is explained bythe simple linear regression yariable is consumption ofnatural gas in millions ofcubicfeet model. [Fuelcons} and the independentyariable is the temperature {Temp}, measured in degrees Fahrenheit. E. This yalue has no practical interpretation. Using the following lylegaStat output, identifythe coefficient of lA—ILJ determination and the correlation coefficient. and interpret each of them. 7 .lnterpret Simple Regression lElutput - Inference BE. Avery broad consensus has emerged around the proposition that global warming is a reality, with likely serious global consequences. Moreover. while there is still not unanimity that global warming is entirely man-made. there is broad agreementthat it is desirable to cut emissions from coal and petroleum. Finally. many energy economists and political leaders are advocating a multipronged approach to providing alternative energy including nuclear, natural gas, clean coal, and renewable sources from solar and wind. Municipalities and states have been asked bythe Department of Energy to assess their energy requirements for each ofthe alternative fuels. In particular, they have decided to focus initially on natural gas. given the enormity oleB. reserves and its relative cleanliness. The regression outputfor selected municipalities in Illinois for “ID reporting periods {weeks} is attached below. The dependent variable is consumption ofnatural gas in millions of cubicfeet [Fuelcons} and the independent variable is the temperature {Temp}, measured in degrees Fahrenheit. Use the attached lulegaStat output to identify and interpret the p—value and the confidence interval forthe regression coefficient. Welcome. Katie Bo Wed Feb 32 Exercise ‘ p-value forthe regression coefficient = ELIZIIZIEIE Round your final answer to four decimal places. Interpretation ofthe p-value forthe regression coefficient: A. This is the probability of correctly concluding thatthere is a relationship between fuel consumption and temperature. E. This is the probability ofbeing incorrect in concluding thatthere is a relationship between fuel consumption and temperature. C. This is the probability ofbeing incorrect in concluding thatthere is no relationship between fuel consumption and temperature. D. This is the probability ofcorrectly rejecting the null hypothesis, that there is a relationship between fuel consumption and temperature. E. This value has no practical interpretation. [3—1: 95% confidence interval = [ , ] Round your final answers to fourdecimal places. i C. Interpret Simple Regression Output - Inference E? E Avery broad consensus has emerged around the proposition that global warming is a reality. with likely serious glooal consequences. Moreover. while there is still not unanimitythat global warming is entirely man—made. there is broad agreement that it is desirable to cut emissions from coal and petroleum. Finally. many energy economists and political leaders are advocating a multipronged approach to providing alternative energy including nuclear. natural gas. clean coal. and renewable sources from solar and wind. Municipalities and states have been asked by the Department of Energyto assess their energy requirements for each ofthe alternative fuels. In particular. they have decided to focus initially on natural gas. given the enormity ofLJ.5. reserves and its relative cleanliness. The regression output for selected municipalities in Illinois for ‘IEI reporting periods {weeks} is attached below. The dependent variable is consumption ofnatural gas in millions of cuhicfeet [Fuelconsl and the independent variable is the temperature [‘I'emp}. measured in degrees Fahrenheit. Use the attached lylega5tat outputto identify and interpretthe p-value and the confidence interval forthe regression coefficient. £7 . Simple LinearRegressionehalysis C‘i-C2Jtlsx - I Welcome. Katie Bot Wed Feb 3 EE Exercise1 Interpretation ofthe 95% confidence interval forthe regression coefficient: A. This says we are 95% confident that. forthe given temperature of 44 degrees. the fuel consumption will be between these values. E. This says we are 95% confident that in the population each additional degree ofincrease in temperature will result in an increase offuel consumption between these values. C. This says we are 95% confident that in the population each additional degree ofincrease in temperature will result in a decrease offuel consumption between these values. D. This says we are 95% confident that over manyweeks. the mean fuel consumption will he between these values. E. This confidence interval has no practical interpretation. Cpl: 7 C. Interpret Simple Regression lDutput - Inference E. A very broad consensus has emerged around the proposition that global warming is a reality. with lilter serious global consequences. Moreover. while there is still not unanimity that global warming is entirely man—made. there is broad agreement that it is desirable to cut emissions from coal and petroleum. Finally. many energy economists and political leaders are adyocating a multipronged approach to proyiding alternatiye energy including nuclear, natural gas. clean coal. and renewable sources from solar and wind. Municipalities and states have been aslted by the Department of Energyto assess their energy requirements for each ofthe alternatiye fuels. In particular. they have decided to focus initially on natural gas. given the enormity ole.9. reseryes and its relative cleanliness. The regression output for selected municipalities in Illinois for ‘IEI reporting periods {weeks} is attached below. The dependent variable is consumption ofnatural gas in millions of cubicfeet [Fuelcons} and the independentyariable is the temperature [‘I'emp}. measured in degrees Fahrenheit. Use the following lylegaStat output to identify and interpret the confidence and prediction interyals for a temperature of 44 degrees Fahrenheit. ii ; Simple LinearRegressionfinalysis C1-CE.xlsx :I Ill Welcome. Katie Bo Wed Feb 32 Exercise: 95% confidence interyal = [ , ] Round your final answers to four decimal places. Interpretation ofthe 95% confidence interyal: A. This says we are 95% confident thatforthe giyen temperature. in any particularweelt. the fuel consumption will be between these yalues. E. This says we are 95% confident that in the population each additional degree ofincrease in temperature will result in a decrease offuel consumption between these values. C. This says we are 95% confident thatforthe given temperature. oyer many weelts. the mean fuel consumption will be between these yalues. D. This says that when the temperature is 44 degrees {Fahrenheit}. the predicted fuel consumption will be 19.99TE million cubicfeet of natural gas. E. This has no practical interpretation in this problem situation. I: v 95% prediction interval = [8.2494 , 11.9549 ] Round your final answers to four decimal places. 7 i2. Interpret Simple Regression lEititptit - Inference E. A yery broad consensus has emerged around the proposition that global warming is a reality. with likely serious global consequences. Moreover. while there is still not unanimitythat global warming is entirely man—made. there is broad agreementthat it is desirable to cut emissions from coal and petroleum. Finally. many energy economists and political leaders are advocating a multiprdnged approach to providing alternatiye energy including nuclear, natural gas. clean coal. and renewable sources from solar and wind. Municipalities and states haye been asked bythe Department of Energy to assess their energy requirements for each ofthe alternative fuels. In particular. they have decided to focus initially on natural gas. given the enormity ofU.9. reseryes and its relative cleanliness. The regression outputfor selected municipalities in Illinois for 19 reporting periods {weeks} is attached below. The dependent yariable is consumption ofnatural gas in millions ofcubicfeet [Fuelcdns} and the independentyariable is the temperature {Temp}. measured in degrees Fahrenheit. Use the following lylega9tat outputto identify and interpretthe confidence and prediction inter'yals for a temperature ofdrdr degrees Fahrenheit. —u ii ; Simple LinearFtegressionAnalysis (St-Chris: Welcome. Katie Bo Wed Feb 3 2 Exercise: «Jun: piuuiuuuiinuuivui —L--—--- ! ---——-— J Round your final answers to four decimal places. Interpretation ofthe 95% prediction inter'yal: A. This says we are 95% confidentthatforthe given temperature. in any particularweek. the fuel consumption will be between these values. E. This says we are 95% confidentthat in the population each additional degree ofincrease in temperature will result in a decrease offuel consumption between these yalues. C. This says we are 95% confidentthatforthe given temperature. dyer many weeks. the mean fuel consumption will be between these values. D. This says thatwhen the temperature is 44 degrees {Fahrenheit}. the predicted fuel consumption will be 19.99735 million cubicfeet of natural gas. E. This has no practical interpretation in this problem situation. A%l;J Regreeeientfltnelyeie r2 [1.336 n 11] r 43.915 I-t 1 Std. Errer ELTEE Dep. 1Inter. FuelCDne AN OVA te ble ......... Reeiduel 4.5965 8 EILEEN El Tetel 28.?040 Regreeeien eutEut confidence r'rrterver' eeeebtee eeet‘ftetefite etd. erTer tfdf=r31 p-eetue 95%tewer 95% upper Intercept 15.2559 [ITEMS 19.282 EASE-US 13.4323 13".0316 TemE -E|_11T3 [1.0183 45.395 .EIEIEIE 43.1595 -E|_E|T5E| ‘ Predicted ueluee fer: FueICene 95% Confluence tntervet 95% Preetetten tnteruet ‘ ......................... .Ieeee ............ .E'reetetee‘. ................. .teeer ............. .eeeer ............... teeter ............... .eeeer ........... .eeeereee... 44 were 9.5254 tueeee 3.2404 11.9543 0.105 fl Applied ivianagefiai smiaeixhu SecJ e Mom'l . Elle Edit iiew HigtcnJ Ecckmai'k: locls flelp wvlaaming ExerciseeMum'lla Fir-eh, “fl .- - — m — -7 1-» - - 3.1.; x eID=9063598tcoursenav=05tbhcp= if V Georgie P m httpswdms.dawry.edufdrnsJWebPagesfflashfcontentfstudentflearningExercise.aspitkourseIDzdfllfidflfituserIDflZDflUUUBidsslflzlflbfiiroletypezfiTl if _i {u - J E \I 3» UpLoadedContent_MDD-115_UploadedAttachment3_Simple Linear RE Walk me thro h a similar problem a e Insert: Page Layout Formulas Data Review View Add-Ins iArial V 12 V I General V Efilnser‘t V E V A ‘_ 1.. 3 . v ...v . v v 2 This says we are 95% confidentthat, inthe population, LI I S _ .B 5.! I I . ’ . 5m“ 3* DEM: D 5‘ each additional $1 ofbeverage expenditure will resultin an ” “mmary' VII 39' V & VI . . ‘33 is v Formfit' Q' Fii Increase In fwd emendflures between these “N0 values In this Walkethrough we have learned howto use simple linear Font r" Ninnment '7'. “WW” r" - cal” E This confidence interval has no practical interpretation. ’99’953'0” 9mm” ‘0 'dem'fy and 'me’p’em‘? Name andme v L“ 1} Regression Analysis confidence interval forthe regression coetficient. _ _ This says thatwe are 95% confidentthat over numerous _ _ _ " . . ..B C D E F G periods. the mean food expenditures will be between these We have used Dom "W‘JtneS'S 193"”? andFonfidence 'mewals to I ion Analysis values discoverwhetherthe independent variable is Significantly relatedto the dependent variable, andthe magnitude ofthe efiect ofthe independent variable onthe dependentvariable. r’ 0.485 n 24 yThat's right! You have correctly seen that ‘This says we are _ _ |' 0-595 k 1 95% confident that, in the population, each additional $1 of ' The 90”“ 95mm“ or B“ '3': 0 0325 Ski Em}, 151773 Dep_ Van FOODTOT beverage expenditure will result in an increase in food _ _ expendlmre beMeenmese vaiuesv - The p—value =0.002forthe regression coetficient I ble - Interpretation otthe p-value: . This concludes ourwork on me regression coemcientl its p. "This isthe probability oibeing incorrectin concluding thatthere is a I salon ' value, andthe confidence interval ofthe regression coelficient relationéhip Dames“ “30d expenditures flfld beverage ’ ' ’ ' I estimate. on the Whiteboard we summarize what we have 9X99”dltures-" ' ..‘9H§‘......547 530-5239.. "2‘1 892-2???" I accumm'sr‘e‘i - The 95% confidence interval for B. is: [0.0173, 0.0475] mm 1’U53’497'5250 23 I - Interpretation otthe confidence interval: Co t'i . . [w ‘This says we are 95% confident that, in the population, each I n output confidence interval l additional $1 of beverage expenditure WIII result in an increase I GO - “5 m! H {:22} p 95% lower 95% upper in food ex manure between mesa valuesi. .. .. .. i p I 1,?49.22?2 185.8255 9.413 3.59E—[19 1,353.8455 2,134.EU?9 iii Simple Linear Regression Analysis East Star Food Salesxlsx I 0-0325 0-0072 4-552 11002 0-0178 0-0475 .1 = I values for: FOODTOT 95% Confidence intervsi 95% Radiation intervsi . —|—| . ‘ T49... Prediqu upper. lower... upper... " " gi ,UUU 2,5914% 2,530.2??? 25541558 2,263.4.[10 2,931.43? 0.04.2 Read dms.devry.edu _ I .— — v. mean 9799226 Da‘laResiduaIs ‘ Outut ‘ Samle Problem _ Wt. of Evident sample variance 69352002 RE“! I r‘nmnln Mnnr‘nrfl rlniuinlinn '31:: 1mm?) X Find: _coefficient ‘ fleet f Erevious HighIighthl M atgh :3 5e Done ...
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