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DAILY GRADE #9 --- 15 minutes

DAILY GRADE #9 --- 15 minutes. Hand out STUFF Begin Chapter 4. Advanced Placement Statistics Section 4.1: Transforming to Achieve Linearity. EQ: How do you determine what type of regression equation best models your data?.

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DAILY GRADE #9 --- 15 minutes

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  1. DAILY GRADE #9 --- 15 minutes • Hand out STUFF • Begin Chapter 4

  2. Advanced Placement StatisticsSection 4.1: Transforming to Achieve Linearity EQ:How do you determine what type of regression equation best models your data?

  3. Up to this point in the course, all of our data has been modeled by lines.

  4. nonlinear. However many relationships are

  5. Objects thrown in the air parabolic exponential Population growth Sometimes things aren’t what they appear.

  6. Transforming Data --- apply a function to straightennonlinear patterns into linear patterns How to determine if a line is the BEST Model? RECALL: Correlation Coefficient Scatterplot Coefficient of Determination Residual Plot

  7. CALCULATOR ACTIVITY: Part I: Exponential Model • Using L1 for year (after 1970) and L2 number of transistors, create a scatterplot for the data on p. 271 in your text book. Note: Cut x-axis off [2nd ZOOM] AXES OFF • Obtain regression statistics. • Create a residual plot for this data

  8. Your scatterplot shows the growth in number of transistors on a computerchip from 1970 to 2000. Explanatory Variable is year after 1970. Response Variable is number of transistors on computer chips.

  9. Discuss why it appears that the pattern of growthis notlinear. Calculate the natural log of NUMBER OF TRANSISITORS and place it inL3. Ln(L2) L3

  10. Create the scatterplot for L1 and L3. Since logs were taken for the response variable only, we will “back transform” this LSRL to an exponentialmodel.

  11. Calculate the Linear Regression Equation: • Use LinRegL1, L3 to calculate the LSRL.

  12. Paste it in Y1 then graph. 7.41 0.332 Ln(# of trans) = ___ + ___ (yrs since 1970) 0.997 0.995 r = ______ r2 = ______

  13. See p 273 and compare the Minitab output with your output. Would you consider this linear model a good fit for this transformed data? Explain.

  14. Rewrite the LSRL as an Exponential Equation: Step 1: We need to know the exponential equation: y = abx Step 2: Rewrite using properties of logs: Ln (transistors) = 7.41 + 0.332 (yrs since 1970)

  15. RECALL: predtransistors=e(7.41+0.332(years since 1970)) Why do we use base e?

  16. pred trans = ( e(7.41) )(e(0.332(years since 1970)) ) predtrans = (1652.426)(1.394(years since 1970) ) Step 3: Sketch this model over the original scatterplot to see how well it “fits”. Y1 = (1652.426)(1.394)^X

  17. Step 4: Use your model to make the prediction for the Intel Titanium 2 which was released in 2003. [HINT: Use TABLE Function] predtrans=(1652.426)(1.394(33) ) = _____ 95,234,335 • Use the EXPREG function and compare your model to the calculator’s:

  18. Our Exponential Model pred transistor =(_____)(____)(year after 1970) 1652.426 1.394 EXPREG Model from Graphing Calculator pred transistor =(_____)(____)(year after 1970) 1648.77 1.394 How do they compare?

  19. Part II: Power Model • Using L1 for DIST and L2 for period of revolutions create a scatterplot for the data on p. 282 in your text book. Your scatterplot shows the increase in distance from the sun as the period of the revolutions also increases. Explanatory Variable is distance from the sun. Response Variable is period of the revolutions.

  20. Calculate the natural log of DIST and place it L3 and the natural log of period of revolutions and place it L4. • Create a scatterplot of these transformations.

  21. Since logs were taken for both the explanatory and response variables, we will “back transform” this LSRL to a power model. • Calculate the Linear Regression Equation: Ln(per of rev) = _____ + ____(ln(distfromsun)) 0.000254 1.50 0.999 r = _______ 0.999 r2 = ______

  22. Would you consider this linear model a good fit for this transformed data? Although curved pattern is apparent, size of residuals is VERY SMALL.[see p. 284]

  23. Rewrite the LSRL as a Power Equation: Step 1: We need to know the power equation: y = axb Step 2: Rewrite using properties of logs: Ln(per of rev) = 0.000254 + 1.50 (Ln(Dist from Sun)) pred per of rev= e(0.000254 +1.50(Ln (Dist from Sun))) pred per of rev=( e(0.000254) )(e(Ln(Dist from Sun)(1.50)) pred per of rev =(1.000)(Dist from Sun)(1.50)

  24. Step 3: Sketch this model over your originalscatterplot to see how well it fits. Step 4: Use your model to predict the period of revolutions for Xena, a new planet discovered in our solar system July 31, 2005. Xena is at an average of 102.15 astronomical units from our sun. 1032.4 yrs. pred per of rev =(1.000)(102.15(1.50) ) = ________

  25. Use the PWRREG function and compare your model to the calculator’s: Our Power Model 1.50 1.000 predperiod of rev =(______)(Dist)(________) PWRREG Model from Graphing Calculator 1.4999 1.000 predperiod of rev =(______)(Dist)(________) How do they compare?

  26. BAT on AP Exam: interpret a residual plot, discuss coefficient of determination, and use a nonlinear model to make predictions • Assignment: • Complete WS problems • p. 276 #5 Perform ExpReg and Power Regto determine which is best model • p. 285 #11 Perform ExpReg and Power Regto determine which is best model. Use your model to answer d) REMEMBER TO “FEED THE PIG” I TURNED IN $20 TODAY. GOOD JOB!!

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