x, with a range of 1-50 (You can use the randbetween command on excel)

Transcription

1 HW 2, Part 1 Question 1 (In EXCEL) Create a data set with the following characteristics: Sample size: 100 One independent variable: x, with a range of 1-50 (You can use the randbetween command on excel) One response variable: y, Let y = 3 + 3e.02x A) Create a scatter plot of y as a function of x in EXCEL, and save the plot in a word document. B) Use EXCEL to perform a linear regression, 2 nd order polynomial regression, and an exponential regression. On the same word document where you have your plot, record the equations and the R 2 values for each regression. C) Try to explain the trends in regression coefficients. Why does the polynomial regression fit better than the exponential regression, even though the data set was created with an exponential function? Will a polynomial regression fit any data set at least as well as a linear regression? Why? D) If you have some data and want to perform a regression, what will be your criteria for selecting the appropriate type of regression? HW 2, Part 1 1. Open your BMEN 211 folder in a file browser window. 2. Right click in your folder and select New then select Microsoft Excel Worksheet 3. Rename this worksheet BMEN211Lab and open the Excel document. 4. In Sheet1 put the following values in Columns B and C, rows 1 to 9: 5. These values are for the initial time, final time, time step size, the size of the input flow change, the initial tank height, the valve coefficient, and the tank area. These must be in the exact positions as above, columns B and C rows 1 to Click the View tab at the top.

2 7. Find the Macro button on the far right. 8. Click the Macro Arrow button (not the icon) then select Record Macro and enter the macro name RunSimulation and give your macro a shortcut, CTRL-t. 9. Immediately, click the Macro Arrow button (not the icon) and select Record Macro and click Stop Recording. This is important. 10. Click the Macro Icon to open a list of macros. Select your macro from the list (RunSimulation) then hit edit. This should open the VBA editing environment. You can switch back to excel using Alt-Tab. 11. The VBA editing environment looks like this: Note that anything on a line after a single quote is treated as a comment and should appear in green. 12. Put the code below (in the CODE SECTION) into your VBA macro and save your file. Put your name in the title section! This should be a bit of typing exercise. Be very careful when copying. Also, note that the code goes below the green header comments and above the End Sub line (which ends the subroutine declaration) 13. Look at the code. Notice the For statement and If statement. 14. On the File tab select Save As and choose Excel Macro-Enabled Workbook. 15. Run your simulation by hitting Ctrl-t and you should get some data. Make a figure like the following using a scatter plot for T, U, H.

3 16. Put your figure in a Word Doc to print out later. YOU SHOULD PASTE INTO WORD AS PASTE SPECIAL, PICTURE Otherwise any change in the excel document will change the figure in your Word doc. 17. Increase the value for k by.5 and run the simulation. Keep increasing k and running the simulation until the simulation breaks. This happens when the simulation tries to take a square root of a negative number. Change back to the last value of k that worked and run the simulation and make a graph of the result. It should look like: 18. Put both figures in your word doc to turn in. 19. What other change could you make to imrprove the robustness of this simulation method? Put ideas in your word document for section 2. Think about what is happening when it breaks. You are getting the current slope and extrapolating forward for dt seconds (dt=0.01) and when the height goes negative, the square root function is not happy CODE SECTION Sub RunSimulation() ' ' RunSim Macro ' Runs Simulation using parameters ' ' Keyboard Shortcut: Ctrl+t ' Dim t_o As Double ' Initial time Dim t_f As Double ' Final time

4 Dim dt As Double ' time step size Dim A As Double ' Input flow step size Dim h_o As Double ' Initial height Dim k As Double ' Valve coefficient Dim T_A As Double ' Tank area Dim t As Double ' Time value Dim u As Double ' Input flow value Dim h As Double ' Tank height ' This gets values from the spreadsheet into variables t_o = Range("C1") t_f = Range("C2") dt = Range("C3") A = Range("C4") h_o = Range("C5") k = Range("C6") T_A = Range("C7") ' This sets up where the data will go and deletes the old stuff Range("F9") = "T" Range("G9") = "U" Range("H9") = "H" Range("F10:H3000").Delete Range("F10").Select ' Set t and h to their initial values t = t_o h = h_o ' This is a FOR loop, when you know how many times to run For i = 1 To 1 + ((t_f - t_o) / dt) ' This is an IF statement, conditional execution If (t < 0) Then ' This sets the u value for right now u = 0 Else u = A End If ' This writes the values into the spreadsheet Cells(i + 9, "F") = t Cells(i + 9, "G") = u Cells(i + 9, "H") = h

5 ' This updates t and h for the next iteration t = t + dt h = h + dt * (u - k * Sqr(h)) / T_A Next i ' This is the end of the For loop ' Note the indentation levels above. This helps read code! End Sub HW 2, Part 3 1. A process is to be modeled inside a cell. It is theorized that species B diffuses into a cell. It then diffuses into the nucleus where it reacts to form species C. C does not leave the nucleus or react in any way, it accumulates continuously increasing amounts. Assume the following: Molar diffusion rate of B into the cell is D 1 A 1 (C Bo (t)-c B (t)) Molar diffusion rate of B into the nucleus is D 2 A 2 (C B (t)-c Bn (t)) Volume of cell outside the nucleus is V Effective volume of cell in nucleus is V n Reaction rate of B changing to C is V n kc Bn (t) Develop a dynamic model for this system. 2. For the following data: x y Find the following approximate values: y=f(x=170) y=f(x=390) y=f(x=25) y=f(x=500) 3. Total drug in for a second order system response can be given as: y(x)=exp(-2x)-exp(x) Approximate the integral of y(x) using the trapezoidal rule from x=0 to x=5 with N=5.

6 HW 2, Part 4 Open excel. Make a data set with 18 data points with reaction rate R as a function of concentration C. The concentration values should be between 1 and 10 (use randbetween(1,10) and the reaction rate should be the following expression: 5*Conc/(3+Conc)+(RAND()-0.5) This reaction rate expression represents Michaelis-Menten kinetics in the form: with some additional noise on the rate measurement value. Every time you make a change in excel, the random functions change values. Take a snapshot of your data by copying/pasting (paste special values) into two locations, columns E&F and columns H &I. In location M2 and M3 put the text Vmax and Km. In location N2 and N3 put the values 5 and 3. In column J, develop model equations for the modeled rate that depend on the concentration and the values for Vmax and Km in location N2 and N3. N2 and N3 must be anchored using $N$2 and $N$3. In column K, develop equations for the difference between the measure rate and the model rate, squared (use parenthesis around the values then ^2). Use the sum command to find the sum of the errors squared. Put the sum of all the error squared values in cell K22, the sum of that column (use =sum(k3:k20) in cell K22). Your spreadsheet my look like: Now, select your first set of data (E2:F20). Select Home->Sort & Filter ->Sort Smallest to Largest. Repeat for Columns H and I. Next, try a custom sort. Select (E2:F20) and use Home->Sort & Filter -> Custom Sort. Add a level and have it sort by rate after it sorts by concentration.

7 Nonlinear optimization using Solver. Select File-> Options. Select Add-Ins from the left tab list. Select Solver Add-In and hit the Go button (Not OK). Select the solver check box and hit ok. In Data->Solver set the wizard to have Objective function $K$22, set the minimize radio button, and have it change cells $N$2:$N$3. Hit the solve button, then accept the answer. Make the scatter plot for your data and model for your word document. Change the line types so that the data is not connected but the model is. What are your resulting values for Vmax and Km. Do the resulting values for Vmax and Km match your true values? Why or why not. Removal of duplicates. Copy your data set into a different sheet (sheet2). Select Data->Filter-Advanced. Select only the column for C for both list and criteria range. Hit ok. This hides rows where C was evaluated multiple times. Note you can undo this under Data->Filter clear. Make a screen capture of your sheet (alt-prscr) and paste it into your Word doc. Double click the image and select the crop tool to only show the portion like below.

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