Math AHHHH!

[Keylee]

So i figured this belonged in the off topics forum since, it's not rping and it really is off topic.

I am in Pre calc for college and we have to do a project on, graphs.

so my x and y values are

(0, 38)
(10, 37)
(20, 36)
(26, 36.3)
(28, 36.4)

Using two plots (10, 37) and (28, 36.4), I found the slope to be -1/30. B is 112/3. There for y= - 1/30x+37.33.

Does that look right to anyone? And average rate of change can someone explain that to me?

[Oniya]

You might want to try roughly plotting the points out first.  For one thing, you have a change in direction between the first three and the last two.  That eliminates a linear (y=mx+b) equation right off the bat.

[Keylee]

Yeah we are suppose to have a linear line, but the teacher says some of our data may not fit the linear equation and we are suppose to say why and show how, and i can't seem to figure out how to put it in my calculator to show the graph all i get are lines, I think I am suppose to put the numbers in the equation.

It was population numbers she told me to make them smaller by rounding. so its like it starts off in 1980 as 0 and 1990 as 10 and 2000 as 20 and 2006 as 26 and 2008 as 28 ect..

[Vekseid]

It isn't plotting a linear graph. We'd need more information to help properly.

Assuming it fits two lines with a minimum at x=20, the first segment would be y = -.1x + 38 and the second segment would be y = .05x + 35.

[Vekseid]

Err.

If you want to do a naive fit, just use the endpoints, rather than picking two in the middle.

[Keylee]

Hmm....I really have no idea now. See I was absent for a week because I hurt my back and I had to lay down every day I could barely walk and she went over what to do for the projects during that week and it hit her Friday to tell me "Oh yeah... its due today, i forgot to tell you about it when you emailed me." And she went over it with me rather fastly. Math is a bad subject for me to begin with!

But here is what she gave me to do....

Fitting curves to data



The purpose of this project is to be able to recognize data that appears linear.



Find data that you think is linear (at least 5 data points).



Fit a line to the data using technology – you may use your calculator or software such as graphical analysis or excel.  Comment on how linear the data is, making reference to the correlation coefficient “r”

Graph the data along with the line of best fit.



Explain whether the line is a good fit for the data. Refer to the “r”(i.e. the correlation coefficient), the rate of change and the overall shape of the graph,  whether the data is randomly scattered about the line of best fit.  If the line is not a good fit for the data, find a better mathematical model by trying the other regression equations on your calculator under “stat – calc”.





Give an example of extrapolating and interpolating from the data  (given an x, find y).  If the line is not a good fit, you should explain that it is difficult to extrapolate from the data using this particular equation – that the results are not accurate.



Give an example of solving the equation for a given value (given y, find x).



Explain what the slope, the x intercept and the y intercept mean in context.



Give an example of the average rate of change for some interval.



Tell what is a reasonable domain for your function in the real life situation.



Note any conclusions or observations you can draw from the data and the line of best fit.

 

Note any historical or circumstances you know that affect the behavior of the trend line or the data.



The report should be written as if it were a magazine article. Use full sentences and use graphs and equations. The only exception to writing it as a magazine article, is that I would like to see your calculations, so I can double check them.

[Oniya]

If you don't have access to something that lets you do a scatter graph (Excel, or Open Office should do), then good old paper and pencil can give you a rough idea of what a graph looks like.  At the very least it will give you an idea of whether the five points are close to being on the same line.

[Keylee]

I didn't know open office had something for graphs, I think I will sketch it out and see what happens.

I hate math....v.v.

[Trieste]

Math is a necessary evil, for me. :/

That set of data points will do fine, because it doesn't really provide the best set for a best-fit line. The point of a best-fit line is that it hits most of the points. I don't have my graphing calculator with me, so I can't see what those points are doing, but what you want to do is get Excel (or Open Office Calc, I think) to make a best-fit line along your data. Find the equation of that line.

Then you're going to play around with equations that aren't linear. Use stat plot on your calculator to enter the data points (zeroing out the year first was a very good idea) and then use the stat calc to do a quadratic regression, etc, on the data points. Keep plugging the regressions you get into y=, and see if any of the lines fit better. There's your answer there.

If you don't know how to do that with your calculator, we can help around here. I had to do pretty much the exact same project my freshman year for math.

[Keylee]

Yeah, it's an evil for me as well, it dosent help that I want to an Art/music high school and now I am in a tech department for college.Stupid high school!

I drew out the graph and it seems to curve a little.

That's what I need to do! I need to get the regression! I think i know how to, thank you!

[Keylee]

Another question how would i put those in my calculator all I am getting is lines going straight across.

[Trieste]

How would you put which one in your calculator?

[Keylee]

to get the regression? and the scatter plots, I know the teacher showed me home but that was only once. Or is that a long process of finding out what goes where? Man I'm so lost, I should have never hurt my back.

[Trieste]

What model of calculator do you have? TI-83?

[Keylee]

Ti-83 plus,

when i type in what's for Y ijust get lines going across.

[Trieste]

Okay, so apologies if I touch on stuff you've already done, but I'm going to go through it step by step. :)

First thing you do is put your points in, so you press the yellow 2ND and then press the blue Y= button (since you hit 2ND, you're actually pressing STAT PLOT). This will bring up a menu of your plots: Plot 1, Plot 2, Plot 3... For now, you will only need Plot 1, so make sure the cursor is highlighting 1: and hit ENTER. That will bring you to the plot setup screen, that looks like this:



Make sure your cursor highlights the On field and hit ENTER again. This tell the calculator to pay attention to Plot 1. You'll also want to make sure your calculator is set to make it a scatter plot (bunch of dots) and not a line, so next to where it says Type: make sure the top left option is selected - the one that looks like a bunch of dots.

Yours will be a little different from this, in that it will say Xlist: L1 and Ylist: L2. That means that you're using List 1 as your X values and List 2 as your Y values. Let's go and fill those in now. Press 2ND and MODE on your calculator (which really is telling the calculator to QUIT out of that screen).

Now you want to press STAT, which is located near the left arrow in the middle right hand of the keypad. The TI-83 plus has EDIT as the default option under STAT, so just go ahead and hit ENTER again since you want to edit your lists. After you do that, you will see a screen that looks like this:



If you have values in your L1 or L2 columns, clear them out by highlighting the L# at the top of the list, hitting CLEAR, and then pressing the DOWN ARROW. Once all of your lists are clear, you can start entering your data.

Remember that your L1 list is your X values, so you want to enter the X values of all your points (0, 10, 20, 26, 28) in L1. Then go and enter all your Y values under L2 (so it'll be 38, 37, 36, 36.3, 36.4). After that's done, you want to hit Y= and clear out anything in there so that you have no other data interfering in your scatter plot. Then hit GRAPH.

Now, when I did this, my calculator was set on the standard window, which goes from -10 to 10 on both the X and Y axes. Since your data set is outside that range, you might have to change the focus on your graph to be able to see the scatter plot. You can do this by pressing the WINDOW button. Then set your X range to be just outside your data range. You probably want it to be Xmin = -5 and Xmax = 30. If you really want to, you can change Xscl to equal 5, but it doesn't really matter for this particular exercise. Then change Ymin to 30 and Ymax to 40 (since all your Y values are between 30 and 40). Then press GRAPH again to see your nice scatter plot.

To find the line of best fit, perform a linear regression on L1 and L2. This is done by quitting out of your graph (remember you press 2ND and MODE in order to get QUIT) and then pressing STAT and selecting CALC with the RIGHT ARROW key and then ENTER. When you do a regression, you have to tell the calculator what to use. Remember that coordinates go in X,Y format, and the regression function goes in the same order. So after pressing STAT, selecting CALC, and pressing the number 4 (for a linear regression), your screen will say LinReg(ax+b) and then have a blinking cursor. You can press 2ND and number 1 (which will fill in L1), then hit the comma key (above the number 7) to separate the sets of coordinates. Press 2ND and the number 2 to fill in your Y values. Don't hit enter yet! You can use the regression function to plug the regressed function right into your Y= screen by doing this:
- Press the comma key again.
- Press VARS (short for variables)
- Select Y-VARS with the RIGHT ARROW, then press the number 1 (for Function).
- Select which Y= line you want your equation to go to. If you already have something filled into the top Y= line (which you can check by pressing Y=), you might find it useful to press the number 2 and have it fill in the regression in the second Y= line. For the purposes of what we have so far, though, you're going to press 1 right now.

So now your screen should say LinReg(ax+b) L1,L2,Y1. Hit enter. You'll see your regression results pop up. You can look at them in more detail, and you can view your best-fit line by hitting GRAPH again. Try doing a quadratic or cubic regression next and see if those fit your line any better. :)

[Keylee]

OOH thank you so much that was a big help *squeezy hug* I got it all now, i kept forgetting the L1 and L2 :D haha... thanks mucho~

[Oniya]

*is useless with graphing calculators, but can work wonders with Excel*

Darn that new-fangled technology.  We weren't allowed to use graphing calcs in our school.  *looks all curmudgeonly*

[Trieste]

You're welcome, Keylee. :)

*is useless with graphing calculators, but can work wonders with Excel*

Darn that new-fangled technology.  We weren't allowed to use graphing calcs in our school.  *looks all curmudgeonly*

Probably because they thought that you couldn't cheat with an abacus.

*flees*

[Oniya]

Remind me to beat you with my cane next time I visit my in-laws.  ;D