Exponential Regression in f(x) = a e^(bx)

[Tony]

I tried to do an exponential regression problem the result was of the
form of f(x) = a b^x, but I was looking for the format of f(x) = a
e^(bx). What am I missing on the Nspire to do this?

Tony

[Sean Bird]

This form of a regression is one of the special features of the TI-Nspire's Vernier DataQuest app. What you want to do if you've already entered the data in a List and Spreadsheet is to link the data to DataQuest.
If you haven't used DataQuest, there are three views: Meter, Graph, Table. From the table view, you can enter data or you can link the variables that are there to existing variables. I did menu, Data, New Calculated column to get the data for the delta T, the difference in the recorded temperature and the room temperature. This made it so that the exponential regression was actually a good fit. 

To link lists that are already entered, choose menu, Data, New Manual Column, and scroll down to select Link from List.

Hope that helps.

On Dec 6, 2012 6:02 AM, "Tony" <abca...@gmail.com> wrote:

I tried to do an exponential regression problem the result was of the form of f(x) = a b^x, but I was looking for the format of f(x) = a e^(bx). What am I missing on the Nspire to do this?

Tony

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[Sean Bird]

I guess inserting images didn't work as well as it used to. I looked good when I hit send.
I'll try again with a different method.

On Sat, Dec 8, 2012 at 12:20 PM, Sean Bird <covena...@gmail.com> wrote:

This form of a regression is one of the special features of the TI-Nspire's Vernier DataQuest app. What you want to do if you've already entered the data in a List and Spreadsheet is to link the data to DataQuest.
If you haven't used DataQuest, there are three views: Meter, Graph, Table. From the table view, you can enter data or you can link the variables that are there to existing variables. I did menu, Data, New Calculated column to get the data for the delta T, the difference in the recorded temperature and the room temperature. This made it so that the exponential regression was actually a good fit. 

To link lists that are already entered, choose menu, Data, New Manual Column, and scroll down to select Link from List.

 

Hope that helps.

On Dec 6, 2012 6:02 AM, "Tony" <abca...@gmail.com> wrote:

I tried to do an exponential regression problem the result was of the form of f(x) = a b^x, but I was looking for the format of f(x) = a e^(bx). What am I missing on the Nspire to do this?

Tony


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Sean Bird
AP Calculus & Physics,
NHS Adviser & Rocket Team Supervisor
Math & Science Technology Coordinator
Covenant Christian High School
7525 West 21st Street
Indianapolis, IN 46214
Phone: 317/390.0202 x104 Fax: 317/390.6823
Website: http://covenantchristian.org/bird
work Email: sean...@covenantchristian.org
personal Email: covena...@gmail.com
Psalm 111:2 “Great are the works of the LORD, studied by all who delight in them.”

[Travis Bower]

Sean,

In VDQ, minor question, why is it that I can expand the x-axis values with the mouse, but the y-values need to be typed/edited?

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[Sean Bird]

I'm not certain I quite follow the question, are you grabbing the corner of the cell when you are in the table view of DQ? I'm not at my computer currently. I may expect the answer to this to have something to do with the y is the dependent variable.

[Travis Bower]

Maybe these screenshots will help.

[Tony]

I was wanting to enter data in the same as any other regression process; there should be a FitNatural regression without using Vernier software...

Tony

On 12/8/2012 11:29 AM, Sean Bird wrote:

I guess inserting images didn't work as well as it used to. I looked good when I hit send.
I'll try again with a different method.

On Sat, Dec 8, 2012 at 12:20 PM, Sean Bird <covena...@gmail.com> wrote:

This form of a regression is one of the special features of the TI-Nspire's Vernier DataQuest app. What you want to do if you've already entered the data in a List and Spreadsheet is to link the data to DataQuest.
If you haven't used DataQuest, there are three views: Meter, Graph, Table. From the table view, you can enter data or you can link the variables that are there to existing variables. I did menu, Data, New Calculated column to get the data for the delta T, the difference in the recorded temperature and the room temperature. This made it so that the exponential regression was actually a good fit. 

To link lists that are already entered, choose menu, Data, New Manual Column, and scroll down to select Link from List.

 

Hope that helps.

On Dec 6, 2012 6:02 AM, "Tony" <abca...@gmail.com> wrote:

I tried to do an exponential regression problem the result was of the form of f(x) = a b^x, but I was looking for the format of f(x) = a e^(bx). What am I missing on the Nspire to do this?

Tony

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--
Sean Bird
AP Calculus & Physics,
NHS Adviser & Rocket Team Supervisor
Math & Science Technology Coordinator
Covenant Christian High School
7525 West 21st Street
Indianapolis, IN 46214
Phone: 317/390.0202 x104 Fax: 317/390.6823
Website: http://covenantchristian.org/bird
work Email: sean...@covenantchristian.org
personal Email: covena...@gmail.com
Psalm 111:2 “Great are the works of the LORD, studied by all who delight in them.”

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[Sean Bird]

Let's do some math. When you do the a*b^x, the b is available as stat.b
But you want a*e^(c*x)
If stat.b=e^c, then c=ln(stat.b)

[Tony]

You lost me and all of my students with stat.b; TI should add the option...

Tony

[Sean Bird]

After you do a regression, press the VAR button. The statistics variables are stored and available for your further analysis.

[Travis Bower]

I sometimes wish it were b.stat   the salient part is first.  So I just ignore the prefix in my mind and stat.b is now just b.  I tell the students to do likewise.

Maybe they will add it in the next update; seems reasonable to me.  I am glad to learn it is in DQ. I rarely use it, to my shame, and need to explore more.

[Sean Bird]

Did we notice the other regression that is now available in DQ? Proportional, aka direct relation, aka y=mx+b where b=0.
In some ways for those who are just starting with the Nspire, the DataQuest application is a great way to work with data. You don't have to remember to label the list, it already says x and y at the top. The data is already graphed in a nice window. You aren't changing pages, just view from table to graph.

On Dec 8, 2012 7:11 PM, "Travis Bower" <tbo...@dphs.org> wrote:

[Sean Bird]

Okay, I'm at a computer. Yes the screen shots helped. Thanks.
Answer: You can move it if you get your mouse in the right spot. See the images below.


Other fun features that are easy to do with DQ is striking some of the data so you can see how that impacts the regression, moving your cursor to the brackets at the end of the regression enables you to change the amount of the sample that the regression is done over.

[Travis Bower]

Thanks.  So, four options:  double arrow blue bar and four arrow plus.... on each axis.

They are hover sensitive.

Is it a stretch to say DQ is to LS and DS as Scratchpad is to calc and graphs?  Except DQ offers so much more [all the input devices].  But it also provides a quick look at data.

--

[Sean Bird]

Nice. I haven't thought of it like that, but in some ways I quite agree.

[John Hanna]

Hey, Travis. Been quietly listening and Sean’s remarks about DQ are worthy of bookmarks – very educational!

 

But I would not put DQ into the same category as ScratchPad. I think ScratchPad is lame and needs to ‘go away’; not removed…. just subordinated some more: please take it off HOME. Too many ‘beginners’ mistake SP Calculate wit Calculator and Graph with Graphs. I’m sad.

 

     John Hanna

     jeh...@optonline.net

     www.johnhanna.us

     T³ - Teachers Teaching with Technology

     "the future isn't what it used to be."

 

---

[Tony]

I agree with you John, the ScratchPad is lame for most uses. It should be removed...

Tony

[Travis Bower]

Cheer up John, maybe Santa will honor your request. lol

I think your suggestion is excellent.  However, precedent seems to be that there are three ways to do something on Nspire.  Reducing methods!?  Unheard of, preposterous!  Well, maybe TI needs to evaluate what is best for students.  I like the sole button.

We rarely use SP in class since most problems are done in their Chapter Notes and necessitate multiple representations.  

As for the analogy, I want to experiment with the idea to include regression as something a calc can do easy and fast and DQ does that.  With modeling such a big component of Core, I would like my students to be facile with analysis on various platforms.  [I have a .tns doc that guides them to use Calc, LS, DS, Notes to find Regressions.  Now I might include DQ.  More methods is not always best, especially in the early stages, but they can pick which method they like the most.]...rambling now...so signing off.

[TR]

Hi,

I'm not convinced that the scratchpad should go away. Let explain why.

Your core assumption is that the calculator is used only by students at class, performing a set of predesigned Document tasks created by their teacher.

You completely neglect a whole other class of users (and uses) like scientists or college students, who use that calculator (that has a fairly powerful CAS system) to perform various calculations. All that while the calculator is not required or mandated by their school or workplace, they simply want to enjoy the power without the overhead of Document management (create new ones, delete old ones, etc) similarly to how the aging TI-89 works at its Home screen.

True, there's more powerful computer software to do that, however it's often much more expensive and less portable. Why force scientists or college students to manage documents, delete old ones for what is often a "temporary" sort of work in nature.

Just my two cents (that's what I use the nspire cas for)

-- TR

[Daniel Dudley]

I agree.  I know that I use scratch pad a lot because I often don't want to deal with a new document for the simple things that I use a calculator for.  My students are the same. 

Dan

Sent from my iPhone

[Sean Bird]

Which page would you prefer for doing a regression? Here are the options.
1. Calculator - the history is static; it doesn't automatically update.
2. LS = List & Spreadsheet - it does update, but you can't see the graphical representation of the data. You can manually change the data right there in the spreadsheet.
3. DS = Data & Statistics - this has a lot of great Fathom-like features: dynamic data, easy to turn regressions on and off. The biggest issue I've heard for this is were is the r (correlation coefficient)? Answer: Go to a calculator or Notes page and press VAR and choose stat.r
4. Notes - dynamic and it includes the r & r^2 (correlation coefficient) You can see all the details of the regression on one page on the handheld. This isn't true for Calc, LS and certainly not for DS.
5. DQ = DataQuest - it has two additional Curve Fits (it is not called Regression here), you get to see the graph and the regression at the same time. You can Menu, Data, Strike Data (But you sure can't grab it like you can in DS). You can also change the 'size' of the window that is analyzed with the regression by grabbing the brackets (the black arrow will turn white).

Notes: To display the most recent regression equation on a Graph page, I'd recommend pressing VAR in the f1(x) entry line and choosing stat.regeqn(x). Yes you need to put in the 'x'. This is also a nice way to evaluate a regression equation for a particular value. On a calculator or notes page do stat.regeqn(2) to see what the value is there.

From my description you may see which I might prefer based on what I want to do, what I want to explore.

- Sean Bird

[Travis Bower]

Looks good.  Sean, if you have time, maybe make an entry on the nspire.site
Maybe edit and add below.  [John, you had some good pros and cons of Graph vs DS awhile ago...chime in]

6. Graphs - After finding the regression in LS, the function will be stored to f1(x).  This can be graphed along with the data points [colored, but not labeled]: Graph Entry>Scatter Plot>now choose from 'var'.  Another way to graph the regression is to use the variable listed in 'var'  f2(x)=stat.regeqn(x)

--

[John Hanna]

I’ve always preferred doing regressions in L&S: you get the results there and they are updated as you change the data in the same page. You can do more than one regression there, too.

 

‘Showing’ regressions on D&S is easy as pi. You cannot see the ‘results’ but they ARE linked, so changing the data updates the regression as in L&S. Best part is tying in resids and residual squares. D&S is used for plotting and analyzing data. It’s not good for graphing functions. Worst feature: in D&S the points in a data graph can be moved, inadvertently changing the data! Danger, Will Robinson!

[Sean Bird]

It is actually quite nice to enter the data in the x, y (or change the variables by clicking on them) in the DataQuest...

Here is what I wrote a while back in answer of what I think you are asking.

[Jessica Kachur]

Wow, what quick response! 

 

Thanks guys, these all helped.  I think I am gount to use the DataQuest suggestion because when I do it live in class,the numbers pop up beautifully and the numbers are exactly what is in the book!

 

I guess I never used the Dataquest just for graphing and analyzing data!  I was apparently under the impression that the Dataquest App dealt with data brought in through a probe and never thought of it using data already in a lists and spreadsheet page! 

 

Great work, again Sean.  See you in a few weeks!

 

Jess Kachur
T3 Regional Instructor
Muka, CGC, TDI, Retired, CL2, CL3-F, CL3-S, CL3-H, TN-O, WV-N
and
C-ATCH2 Jibay, Sandy Acres lil' Phantom, AAD, AJ, AG, ASA, AS, AR, NA, NAJ, TDI, CGC, ChST, ChSN, ChFH, ChJP, ChJU, ChCO

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[kwee]

May i know : how u get the data on the third column?(change in T)? when i did my experiment, i only get the temperature, not change. did u create it manually?

On Sunday, December 9, 2012 1:20:48 AM UTC+8, Bird wrote:

This form of a regression is one of the special features of the TI-Nspire's Vernier DataQuest app. What you want to do if you've already entered the data in a List and Spreadsheet is to link the data to DataQuest.
If you haven't used DataQuest, there are three views: Meter, Graph, Table. From the table view, you can enter data or you can link the variables that are there to existing variables. I did menu, Data, New Calculated column to get the data for the delta T, the difference in the recorded temperature and the room temperature. This made it so that the exponential regression was actually a good fit. 

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

...

[Sean Bird]

Yes, doing a change in T is important for the data to fit the regression. Delta T is the difference between the temperature and the room temperature. It is called a Calculated Column and you do this through the menu options > Data > New Calculated Column.

Hope that helps,
Sean Bird

On Fri, Feb 22, 2013 at 1:51 AM, kwee <kwe...@hci.edu.sg> wrote:

May i know : how u get the data on the third column?(change in T)? when i did my experiment, i only get the temperature, not change. did u create it manually?

Bird wrote:

[kwee]

i got the part on the creation of the 3rd column, but i still dont get the point of doing 'temperature - room temperature', it is just the original data translated down, so the both sets of data shld give good fit in this case.then what is the purpose of doing it? thanks!

[Sean Bird]

I don't have a nice Nspire document to explain this. But here is a
TI-89 and http://education.ti.com/xchange/US/Math/Algebra/5360/TI-CAS_DL_V05.pdf
TI-84 version of this activity http://www2.vernier.com/sample_labs/EZ-TMP-17-newton_cooling.pdf

I don't have the temperature data on me right now, but if you tried the exponential regression for the original data you would see how bad the curve fit was. Actually, take a look at the first TI-Nspire image below. I think you can see how bad the regression was for the top blue curve and what a great fit it is for the red curve.

For there to be a cooling or heating curve it really doesn't matter what the temperature, but what the difference in temperature is. See the page from a Greg Kelly ppt that explains that the differential equation depends on the difference in temperature. If you live in an area with extreme temperatures you know this from experience. The more the difference in temperature between the inside of your house and the outside, the more work your heating or air conditioner needs to do to maintain that large difference in temperature. This is why many people adjust their thermostat so that in the winter they keep their house cool and in the winter the inside temperature is higher.

[Sean Bird]

      [Sorry, the images failed in sending well. Let's see if this works better.]

I don't have a nice Nspire document to explain this. But here is a
TI-89 and http://education.ti.com/xchange/US/Math/Algebra/5360/TI-CAS_DL_V05.pdf
TI-84 version of this activity http://www2.vernier.com/sample_labs/EZ-TMP-17-newton_cooling.pdf

I don't have the temperature data on me right now, but if you tried the exponential regression for the original data you would see how bad the curve fit was. Actually, take a look at the first TI-Nspire image below. I think you can see how bad the regression was for the top blue curve and what a great fit it is for the red curve.

For there to be a cooling or heating curve it really doesn't matter what the temperature, but what the difference in temperature is. See the page from a Greg Kelly ppt that explains that the differential equation depends on the difference in temperature. If you live in an area with extreme temperatures you know this from experience. The more the difference in temperature between the inside of your house and the outside, the more work your heating or air conditioner needs to do to maintain that large difference in temperature. This is why many people adjust their thermostat so that in the winter they keep their house cool and in the winter the inside temperature is higher.

[Sean Bird]

Attached is the page from the ppt that was cited but not included in the previous email.
Enjoy,
Sean Bird

On Tue, Feb 26, 2013 at 1:11 AM, Sean Bird <covena...@gmail.com> wrote:

    
I don't have a nice Nspire document to explain this. But here is a
TI-89 and http://education.ti.com/xchange/US/Math/Algebra/5360/TI-CAS_DL_V05.pdf
TI-84 version of this activity http://www2.vernier.com/sample_labs/EZ-TMP-17-newton_cooling.pdf

I don't have the temperature data on me right now, but if you tried the exponential regression for the original data you would see how bad the curve fit was. Actually, take a look at the first TI-Nspire image below. I think you can see how bad the regression was for the top blue curve and what a great fit it is for the red curve.

For there to be a cooling or heating curve it really doesn't matter what the temperature, but what the difference in temperature is. See the page from a Greg Kelly ppt that explains (or at least shows) that the differential equation depends on the difference in temperature. If you live in an area with extreme temperatures you know this from experience. The more the difference in temperature between the inside of your house and the outside, the more work your heating or air conditioner needs to do to maintain that large difference in temperature. This is why many people adjust their thermostat so that in the winter they keep their house cool and in the winter the inside temperature is higher.

[Sean Bird]

Attached is the data for any who want to play. For those with the iPad app, it even has the data on other applications then just DataQuest.

On Tue, Feb 26, 2013 at 6:51 AM, Sean Bird <covena...@gmail.com> wrote:

Attached is the page from the ppt that was cited but not included in the previous email.

 

On Tue, Feb 26, 2013 at 1:11 AM, Sean Bird <covena...@gmail.com> wrote:

[kwee]

i tried it out myself and realised that Nspire only fit in exponential curve of the form y= a*b^x...that explains why the transformed data has a good fit whereas the original data has a lousy fit: the original data has asymptote at y=room temp. the transformed data has asym at y=0.