Bus Rides Regression Question

[Kevin]

I was trying to get the best model for this regression and I got a
couple that seem to work, but I'm not sure what makes the best one.
The first regression has the highest F value at over 200 the other two
are at around 160. They all pass T-tests. Does the higher F make the
model better than the other two?




Coefficients Standard Error t
Stat P-value
Intercept 27.30537201 0.606198278 45.04363177 2.49606E-75
PGAS -4.852391695 0.458866368 -10.57473816 1.0405E-18
PPARK 14.64391818 0.720887181 20.31374474 5.20511E-40
RIDERS 0.009479135 0.002840797 3.336787083 0.001139271


Coefficients Standard Error t Stat P-
value
Intercept 28.80400841 0.871493951 33.05130046 1.49939E-60
PGAS -5.877706228 0.62658456 -9.380547504 7.19773E-16
PPARK 15.51109093 0.797507969 19.44944946 3.66741E-38
RIDERS 0.007584038 0.002900957 2.614322403 0.010137223
Reductions -0.969565313 0.412156803 -2.352418562 0.020351451



Coefficients Standard Error t Stat P-value
Intercept 27.30060769 0.592774426 46.05564356 5.97094E-76
PGAS -5.307714325 0.483907084 -10.96845757 1.3613E-19
PPARK 14.0651196 0.741596585 18.96599832 3.35157E-37
RIDERS 0.015008762 0.003543848 4.235159363 4.62323E-05
Spring Sem -0.68567007 0.272862468 -2.512877921 0.013360503


Kevin

[Kevin]

Additionally, my DW stat is really low on all of them... between .2
and .3....

does that mean I need to change my variables more?


Kevin

[Gabriel Bowers]

Kevin,

Here are the coefficients that I ended up with for linear and
log-linear. It seems to me that you need to add in the seasonal
semesters for spring, fall, and winter. You need to only use dummy's
for two of the three months.

My DW was ~1.5 for linear and 1.87 for log-linear.

Also, 14.2% MAPE for linear and 6% MAPE for log-linear looking at part 3.

Linear Regression

Coefficients Standard Error t Stat

Intercept 20.54112391 24.76018568 0.829602984
ENROLL_Fall 6.314828478 0.618696375 10.20666798
PBUS -230.2342637 46.13069201 -4.990912854
PGAS 68.22733274 7.106934461 9.600107208
Spring 15.78812535 3.573676655 4.417894195
Summer -51.00263181 3.403230314 -14.98653547
July86 -29.9584818 6.833298602 -4.384190351

Log-Linear

Coefficients Standard Error t Stat

Intercept 2.494072831 0.551901294 4.519055959
ln_ENROLL_Fall 0.651844821 0.166430137 3.916627327
ln_PBUS -0.58422463 0.114662403 -5.095171686
ln_PGAS 0.390094878 0.060138735 6.486582725
ln_Spring 0.073139064 0.018946383 3.860317919
ln_Summer -0.346102602 0.018078768 -19.1441471
ln_July86 -0.232899291 0.036099016 -6.451679752
ln_PPARK 0.024725655 0.01212977 2.038427312

[Kevin]

I had the spring and summer dummys

For the dummy variable on Jan 1985 and July 1986 did you just put 1's
after those months til the end?

[Elliott Le]

Hey Kevin,

That should do it.

Also, what do we do with dummy variables for the log-linear model? Add 1 or just leave it alone? Taking the log won't do it.

Elliott Le

--
Elliott Le

[Gabriel Bowers]

You should use 1's and 0's for linear and log-linear.

Gabriel

[zhouz...@yahoo.com]

HI Garriel , why don't you use jan 85, and when using dummy
spring and summer , put 1 on corresponding monthes ,and 0 on
ohters right ?

On Mar 13, 5:17 pm, Gabriel Bowers <gabrielbow...@gmail.com> wrote:
> You should use 1's and 0's for linear and log-linear.
>
> Gabriel
>
>
>
> On Sun, Mar 13, 2011 at 4:54 PM, Elliott Le <elliott...@gmail.com> wrote:
> > Hey Kevin,
> > That should do it.
> > Also, what do we do with dummy variables for the log-linear model? Add 1 or
> > just leave it alone? Taking the log won't do it.
> > Elliott Le
>

> > Elliott Le- Hide quoted text -
>
> - Show quoted text -

[Kevin]

I wasn't sure about that either.. my model kept jan 85....




On Mar 14, 10:59 am, "zhouziha...@yahoo.com" <zhouziha...@yahoo.com>
wrote:

[Adi Aloni]

I just did this problem, too. I detailed my findings below. However, I
wanted to ask what is your reply regarding "is automobile transportation a
substitute for bus transportation"?
Adi.

For the linear model:
Coefficients
Intercept 81.89400815
ENROLL 3.062494289
PBUS -241.9191402
PGAS 37.33700701
PPARK 71.30472327
Fall 52.44882116
Spring 67.68761253
1985 -14.7988598
1986 -26.96257142

For the log linear model:
Coefficients
Intercept 2.378023309
Ln(ENROLL) 0.602554856
Ln(PBUS) -0.542214453
Ln(PGAS) 0.319234529
Ln(PPARK+0.01) 0.029582812
Fall 0.345760213
Spring 0.420880418
1985 -0.053767567
1986 -0.214064841

[Robert Binkley]

Hi Guys,

I just ran though this regression and have not been able to find a linear regression that passes the DW test (i.e. there is serial correlation in the residuals and I cant find it). Has anyone come up with a successful linear regression for the Bus Rider problem?

Rob

-----Original Message-----
From: econ_401_w...@googlegroups.com [mailto:econ_401_w...@googlegroups.com] On Behalf Of zhouz...@yahoo.com
Sent: Monday, March 14, 2011 10:59 AM
To: Econ_401_winter_2011
Subject: Re: Bus Rides Regression Question

This email and any attachments are intended for the sole use of the named recipient(s) and contain(s) confidential information that may be proprietary, privileged or copyrighted under applicable law. If you are not the intended recipient, do not read, copy, or forward this email message or any attachments. Delete this email message and any attachments immediately.

[Adi Aloni]

Hi Rob,
My DW is 1.65, which is acceptable. I attach the excel of you want to see
the calculations.
Adi.

[zhouz...@yahoo.com]

MY t -test shows Jan Jul and PPARK all failed ,I think we might
need to compare the price elasticity between bus and gas,
since parking has no impact ,.

>  rider.xlsx
> 111KViewDownload- Hide quoted text -

[Adi Aloni]

Do we seriously have to remember the formula for estimating demand for an
innovation?

Also does anyone have any insights from the tutoring session on Saturday, if
there was one?

Thanks,
Adi.

[Robert Binkley]

Hi Adi,

Yours looks good. I must have messed something else up...

-r

[Carla Nunes]

Hey guys,

I haven't started on the regressions yet.  I'll try to run mine later this afternoon, and will provide some input.

Adi, w/ regards to your question, yes, we'll need to memorize the formula for the diffusion model... in the TA session, she didn't say which regression it'll be in the exam.  She only mentioned that if we had to do the one for innovation it would be easier as the variable are pretty much set.

In my opinion, I believe the regression will be a "regular" regression in which we'll have to choose the variables to be included.

BTW, the regression is worth 40% of the final.

Carla

[Spencer Hsu]

is anyone going to be on campus after 8 to meet up?

[Christy Fairlie]

I'm doing Econ study now til 6 and then again after 11.  I'm in Lucas now and will be at the library after 11 if anyone wants to meet up with me.

Christy

[Adi Aloni]

Has anyone looked at the TIO2 or Polyethylene problems and can share
findings?

[Carla Nunes]

Hi Adi,

The TA mentioned to not look at those.  Also, the following are out:  Learning Curve, Dioxide, Oakland A's

These are the ones we're supposed to do:

Bus rides
Gasoline
VCRs
Audio – price discrimination
Sales force – marginal analysis
Metrics system – pricing strategy
Bookstore – relevant cost
Cross training – contribution margin for multiple products
Marketing team – optimal pricing
Hotel price – price elasticity


Carla

[Samuel Harrison]

Hey all -- in particular Adi - 

I just ran through this regression - or at least enough to have a good feel for it.

My numbers were CLOSE to what you had, but not exactly.  Any ideas for the difference?

Mine:

Linear:

	Coefficients
Intercept	82.21356266
ENROLL	3.092547875
PBUS	-242.8055947
PGAS	36.63668358
PPARK	71.8761977
Fall	51.08185769
Spring	69.01120318
1985	-10.00632953
1986	-23.88962779

Log:

	Coefficients
Intercept	2.403905904
ln(Enroll)	0.598941443
ln(pbus)	-0.533099756
ln(pgas)	0.304878531
ln(ppark+.01)	0.030578823
Fall	0.335014695
Spring	0.431751055
1985	-0.033894156
1986	-0.162664781

Thanks for your help!

Attached is my version if you want to poke around.

Sam

[Samuel Harrison]

I must have missed the day we covered the formula for estimating demand for an innovation.

Does anyone have that handy or can they direct me to where I can find it in the book or the slides?  Haven't been able to find it.

Thanks!

Sam

[Adi Aloni]

Go to class slides on Eres, Diffusion/Lifecycle Models. Only the logistic model is relevant.

[Adi Aloni]

Thanks, that’s a relief…

 

From: econ_401_w...@googlegroups.com [mailto:econ_401_w...@googlegroups.com] On Behalf Of Carla Nunes

Sent: Monday, March 14, 2011 2:59 PM
To: econ_401_w...@googlegroups.com

[Samuel Harrison]

Awesome - thanks - I was just about there with my review of the slides.

[Adi Aloni]

I got it – the 1968 variable starts on July, not January.

[Samuel Harrison]

Ah HA!

Thanks for your help.  That was just an error of me putting in the dummy var.

[Sam]

Adi,

I got the same answers as you except the RMSE. I noticed you divided
the squares by 12 (the number of observations). The denominator of
RMSE is m-k, so I think it should be 12-8=4 since we have 12
observations and 8 coefficients from the regression. So my RMSE
calculates to 16.69.

On Mar 14, 3:22 pm, Samuel Harrison <samuelpharri...@gmail.com> wrote:
> Ah HA!
> Thanks for your help.  That was just an error of me putting in the dummy
> var.
>

> On Mon, Mar 14, 2011 at 3:15 PM, Adi Aloni <aloni....@gmail.com> wrote:
> > I got it – the 1968 variable starts on July, not January.
>

> > *From:* econ_401_w...@googlegroups.com [mailto:
> > econ_401_w...@googlegroups.com] *On Behalf Of *Samuel Harrison
> > *Sent:* Monday, March 14, 2011 3:00 PM
>
> > *To:* econ_401_w...@googlegroups.com
> > *Subject:* Re: Bus Rides Regression Question

>
> > Hey all -- in particular Adi -
>
> > I just ran through this regression - or at least enough to have a good feel
> > for it.
>
> > My numbers were CLOSE to what you had, but not exactly.  Any ideas for the
> > difference?
>
> > Mine:
>
> > Linear:
>

> > * *
>
> > *Coefficients*

>
> > Intercept
>
> > 82.21356266
>
> > ENROLL
>
> > 3.092547875
>
> > PBUS
>
> > -242.8055947
>
> > PGAS
>
> > 36.63668358
>
> > PPARK
>
> > 71.8761977
>
> > Fall
>
> > 51.08185769
>
> > Spring
>
> > 69.01120318
>
> > 1985
>
> > -10.00632953
>
> > 1986
>
> > -23.88962779
>
> > Log:
>

> > * *
>
> > *Coefficients*

> > > >> > Intercept       <20.54112391>20.54112391     24.76018568
> > 0.829602984
> > > >> > ENROLL_Fall     <6.314828478>6.314828478     0.618696375

> > 10.20666798 PBUS
> > > >> > -230.2342637     46.13069201     -4.990912854 PGAS

> > > >> > <68.22733274>68.22733274       <7.106934461>7.106934461
> > 9.600107208 Spring
> > > >> > 15.78812535      3.573676655     <4.417894195>4.417894195 Summer

>
> > > >> > -51.00263181    3.403230314     -14.98653547
> > > >> > July86                 -29.9584818      6.833298602

> > > >> > - <4.384190351>4.384190351

>
> > > >> > Log-Linear
> > > >> >                        Coefficients     Standard Error  t Stat
> > > >> > Intercept       2.494072831     0.551901294     4.519055959
> > > >> > ln_ENROLL_Fall  0.651844821     0.166430137     3.916627327

> > > >> > ln_PBUS -0.58422463     0.114662403     - <5.095171686>5.095171686ln_PGAS

> > > >> > > > 0.606198278     <45.04363177>45.04363177

> > > >> > > > 2.49606E-75
> > > >> > > > PGAS    -4.852391695    0.458866368     -10.57473816
> >  1.0405E-18
> > > >> > > > PPARK   14.64391818     0.720887181     20.31374474
> > 5.20511E-40
> > > >> > > > RIDERS  0.009479135     0.002840797     3.336787083
> > 0.001139271
>
> > > >> > > >                 Coefficients    Standard Error       t Stat
> > > >> > > >         P-
> > > >> > > > value
> > > >> > > > Intercept       28.80400841     0.871493951     <33.05130046>

> > 33.05130046
> > > >> > > > 1.49939E-60 PGAS    - <5.877706228>5.877706228    0.62658456

>
> > > >> > > > -9.380547504
> >  7.19773E-16
> > > >> > > > PPARK   15.51109093     0.797507969     19.44944946
> > 3.66741E-38
> > > >> > > > RIDERS  0.007584038     0.002900957     2.614322403
> > 0.010137223
> > > >> > > > Reductions -0.969565313 0.412156803     -2.352418562
> >  0.020351451
>
> > > >> > > >                 Coefficients    Standard Error       t Stat
> > > >> > > >        P-value
> > > >> > > > Intercept       27.30060769     0.592774426     46.05564356
> > > >> > > > 5.97094E-76

> > > >> > > > PGAS    - <5.307714325>5.307714325    0.483907084

[Carla Nunes]

Sam,

Both are divided by the number of observations being forecasted, which in this case is 12.

See slide 7 in regression 2 slides.  (N-m)

Carla

[Carla Nunes]

Hi guys,

Qq, when doing the log-linear, I find that the 1985 dummy does not pass the t-test, so it should be removed.  Does anybody get the same?

Carla

[Gabriel Bowers]

Yes.  I also failed 1985.

[Carla Nunes]

Ok, my log linear model has same variables as the linear one, but does not have the 1985 dummy.

[Kevin]

If we use different semesters for the dummy say some use spring and
fall and someone else uses summer and fall that will make our
coefficients different? correct?


Kevin

On Mar 14, 7:02 pm, Carla Nunes <ccrnu...@gmail.com> wrote:
> Ok, my log linear model has same variables as the linear one, but does not
> have the 1985 dummy.
>

> On Mon, Mar 14, 2011 at 6:39 PM, Gabriel Bowers <gabrielbow...@gmail.com>wrote:
>
>
>
>
>
>
>
> > Yes.  I also failed 1985.
>

> > On Mon, Mar 14, 2011 at 6:00 PM, Carla Nunes <ccrnu...@gmail.com> wrote:
>
> >> Hi guys,
>
> >> Qq, when doing the log-linear, I find that the 1985 dummy does not pass
> >> the t-test, so it should be removed.  Does anybody get the same?
>
> >> Carla
>

> >> On Mon, Mar 14, 2011 at 5:34 PM, Carla Nunes <ccrnu...@gmail.com> wrote:
>
> >>> Sam,
>
> >>> Both are divided by the number of observations being forecasted, which in
> >>> this case is 12.
>
> >>> See slide 7 in regression 2 slides.  (N-m)
>
> >>> Carla
>

> >>>> > > <3.092547875> <3.092547875> <3.092547875>3.092547875

>
> >>>> > > PBUS
>
> >>>> > > -242.8055947
>
> >>>> > > PGAS
>
> >>>> > > 36.63668358
>
> >>>> > > PPARK
>
> >>>> > > 71.8761977
>
> >>>> > > Fall
>

> >>>> > > <51.08185769> <51.08185769> <51.08185769>51.08185769

>
> >>>> > > Spring
>
> >>>> > > 69.01120318
>
> >>>> > > 1985
>
> >>>> > > -10.00632953
>
> >>>> > > 1986
>
> >>>> > > -23.88962779
>
> >>>> > > Log:
>
> >>>> > > * *
>
> >>>> > > *Coefficients*
>
> >>>> > > Intercept
>

> >>>> > > <2.403905904> <2.403905904> <2.403905904>2.403905904

> >>>> > > > >> > Intercept       < <20.54112391> <20.54112391> <20.54112391>
> >>>> 20.54112391> <20.54112391> <20.54112391> <20.54112391>20.54112391
> >>>> 24.76018568
> >>>> > > 0.829602984
> >>>> > > > >> > ENROLL_Fall     < <6.314828478> <6.314828478> <6.314828478>
> >>>> 6.314828478> <6.314828478> <6.314828478> <6.314828478>6.314828478

> >>>> 0.618696375
> >>>> > > 10.20666798 PBUS
> >>>> > > > >> > -230.2342637     46.13069201     -4.990912854 PGAS

> >>>> > > > >> > < <68.22733274> <68.22733274> <68.22733274>68.22733274><68.22733274><68.22733274><68.22733274>
> >>>> 68.22733274       < <7.106934461> <7.106934461> <7.106934461>
> >>>> 7.106934461> <7.106934461> <7.106934461> <7.106934461>7.106934461
> >>>> > > 9.600107208 Spring
> >>>> > > > >> > 15.78812535      3.573676655     < <4.417894195><4.417894195><4.417894195>
> >>>> 4.417894195> <4.417894195> <4.417894195> <4.417894195>4.417894195Summer

>
> >>>> > > > >> > -51.00263181    3.403230314     -14.98653547
> >>>> > > > >> > July86                 -29.9584818      6.833298602

> >>>> > > > >> > - < <4.384190351> <4.384190351> <4.384190351>4.384190351><4.384190351><4.384190351><4.384190351>

> >>>> 4.384190351
>
> >>>> > > > >> > Log-Linear
> >>>> > > > >> >                        Coefficients     Standard Error  t
> >>>> Stat
> >>>> > > > >> > Intercept       2.494072831     0.551901294     4.519055959
> >>>> > > > >> > ln_ENROLL_Fall  0.651844821     0.166430137     3.916627327

> >>>> > > > >> > ln_PBUS -0.58422463     0.114662403     - < <5.095171686><5.095171686><5.095171686>
> >>>> 5.095171686> <5.095171686> <5.095171686> <5.095171686>5.095171686
> >>>> ln_PGAS

> >>>>  > > > >> > 0.390094878     0.060138735     6.486582725 ln_Spring
> >>>> > > > >> > 0.073139064     0.018946383     3.860317919 ln_Summer
> >>>> > > > >> > -0.346102602    0.018078768     -19.1441471
> >>>> > > > >> > ln_July86       -0.232899291    0.036099016     -6.451679752

> >>>> > > > >> > ln_PPARK        0.024725655     0.01212977       <<2.038427312><2.038427312><2.038427312>
> >>>> 2.038427312>
> >>>> > > <2.038427312> <2.038427312> <2.038427312>2.038427312

> ...
>
> read more »

[Carla Nunes]

That's correct, Kevin.  This happens because your "base" semester changed.