2.8 Polynomial Models in the Real World€¦ · Model Data with a Polynomial Function ‐Regression Analysis: Get out your TI‐84: Press the “STAT” button. Under the first heading

Sec 3 Honors 2.8.notebook

2.8 Polynomial Models in the Real World

• Use data and write a function to represent the data.• Analyze which model fits data the best.


Solve It!


So we know this data comes from a quadratic equation, but what is the equation? Let's use our calculator to find out.

First go to the "STAT" button & under "EDIT" type in the lengths in L1 & the areas in L2.

Then go to the "STAT" button & this time under "CALC" go to 5: QuadReg & hit enter.

The amazing calculator will figure out the equation!!!

Notice the graph of the quadratic goes right through all the points.

53


Let's try doing the differences for this set of points (on page 119):


Even though we can't tell what kind of equation we have by doing the differences, we can still put the points in our calculator and do a regression analysis to find the best fitting polynomial function.

The polynomial with the best fit will have an R2 value closest to one.

(R2 is the "coefficient of determination." You must turn on diagnostics for this to show up - Go to "Catalog" & then "DiagnosticsOn" & hit enter.)


But is it really?


Let's put this set of points in our calculator & do a regression analysis.

How many points are in our data set? What polynomial had an R2 value closest to 1?


Be careful though, just because it has three points, for example, doesn't mean that the quadratic is always the best fit! Remember you want to get the best R2 value that still makes sense with the data given.(For example: our "solve it" for today was quadratic, but it had more that 3 points.)


Model Data with a Polynomial Function ‐Regression Analysis:

Get out your TI‐84:Press the “STAT” button.Under the first heading “EDIT” selection option “1 Edit” and push enter.Delete all of the entries in each list (L1, L2, …). Put the curser over an entry (not the L1 or L2) and push delete.ORPut the curser over the list heading at the top like”L1” and push clear and then enter. Do not push delete (the entire L1 list will be deleted) Now that your lists have been deleted you need to enter your new information. Put the x into L1 and the y into L2. Also, if you are entering years like 1990 and 1992, then you would enter 90 and 92.Now that your list is entered push “STAT” and go to the second heading of “CALC”. Under “CALC” you will choose options: 4 LinReg (to see if it is a straight line), 5 QuadReg (to see if it is a quadratic), 6 CubicReg (to see if it is cubic), or 7 QuartReg (to see if it is quartic).Choose the model with R2 closest to 1 that makes sense for the given data. Use the numbers given for a , b, c and ….etc to write your equation ‐ round to 3 decimal places.

To put the equation you got on the regression analysis into y= in your calculator:Right after getting the regression equation press the y= button & clear out any equation in there.Then press the "Vars" button & then "5:statistics". Then arrow over on the top to "EQ" & press enter on "1:RegEQ". The equation will go into your y= window & now you can graph it.


When doing regression lines, round to 3 decimal places.

However, you can't round to zero, so if that is the case, use more decimals for that term only.


(This problem is not in your book.)


Why would a linear model work best for this set of data? We have 3 points, why not try a quadratic model?



What cubic model best fits the data?

Use the model to estimate a value for the year 2012.

3. US Federal Spending


What is interpolation?

What is extrapolation?

Which do you think provides more accuracy?


Compare regression models to determine which one best fits the data.

Which model seems more likely to represent the data?

5. US Homes

7. Estimate the average sale price for homes sold in the United States for 1985, 1999, and 2020.


9. Determine which type of model best fits the set of points.

(2, 1), (0, 3), (2, 7)


Assignment: Section 2.8: problems 1015, 17, 1921, & 27

#1012: You must write out the equation you got on the calculator as your work on the

homework.

#14: Give an actual explanation, not just the equation.

#20: Plot points on the calculator. Then decide which model is better for the situation & use the

model to make the prediction.

#27d TYPO on answer key: should say 4.2%

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2.8 Polynomial Models in the Real World€¦ · Model Data with a Polynomial Function ‐Regression Analysis: Get out your TI‐84: Press the “STAT” button. Under the first heading