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’nE residueHuff regressien
:52 find the sqn‘ residuei H fetei 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 manmade, 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 EIlElBJtlsx
l lu'llelcorrie. ltmlr 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 : it. 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 manmade, 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 EI1EIBxlsx
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: lll 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
94 453 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 3133: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 manmade. 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 ‘ pvalue forthe regression coefﬁcient = ELIZIIZIEIE Round your ﬁnal answer to four decimal places. Interpretation ofthe pvalue 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 pvalue
and the conﬁdence interval forthe regression coefﬁcient. £7 . Simple LinearRegressionehalysis C‘iC2Jtlsx
 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 C1CE.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 (StChris: 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 It 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 peetue 95%tewer 95% upper Intercept 15.2559 [ITEMS 19.282 EASEUS 13.4323 13".0316
TemE E_11T3 [1.0183 45.395 .EIEIEIE 43.1595 E_ET5E ‘ 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 Fireh, “ﬂ .  — m — 7 1»   3.1.; x eID=9063598tcoursenav=05tbhcp= if V Georgie P
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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 _ _ ' 0595 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 pvalue:
. 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 5305239.. "2‘1 8922???"
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 00325 00072 4552 11002 00178 00475
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= 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
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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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 Fall '10
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 Linear Regression, Regression Analysis, Global Warming, ........., natural gas., consumption ofnatural gas

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