Nonlinear Regression Act4 Exponential Predictions (Statcrunch)

Transcription

1 Nonlinear Regression Act4 Exponential Predictions (Statcrunch) Directions: Now that we have established the exponential relationships with these variables and analyzed the residuals, let s use the equations we found in Statcrunch to make predictions. Now, this will be a little difficult since Statcrunch does not really solve for y. We will need to solve the natural log equation to get our predicted values. Any time we are making predictions we need to keep the scope of the data in mind and not go too far outside of the scope (excessive verses reasonable extrapolation). 1. We looked at the relationship between the years since 1995 (x) and world-wide wind power capacity in MW (megawatts) (y). Statcrunch gave the following exponential equation and scatterplot. Since this is a reasonably good model, let s use the equation to make some predictions. LN ( y ) = ( x ) a) What is the scope of the data (x values)? What years does the scope represent? b) Do you think Wind Power will continue to follow this pattern into the future? Why or why not? Discuss the implications on extrapolation. How far do you think you can extrapolate before the prediction becomes really bad? Why? c) Solve the logarithmic equation to predict the Wind Power in 2002 (year 7)? d) Solve the logarithmic equation to predict the Wind Power in 2008 (year 13)? world wide wind power in 2015 (year 20)? Why or why not? If you said yes, then go ahead and make the prediction and see if the answer looks reasonable or not.

2 2. We looked at the relationship between months since January 1 st 2010 (x) and a retirement account balance in thousands of dollars (y). Statcrunch gave the following exponential equation and scatterplot. Since this is a reasonably good model, let s use the equation to make some predictions. Ln ( y ) = (x) a) What is the scope of the data (x values)? What months does the scope represent? b) Do you think the retirement account balance will continue to follow this pattern into the future? Why or why not? Discuss the implications on extrapolation. How far do you think you can extrapolate before the prediction becomes really bad? Why? c) Solve the exponential equation to predict the retirement account balance December 15 th 2010 (month 11.5)? d) Solve the exponential equation to predict the retirement account balance January 15 th 2012 (month 24.5)? retirement account at the start of 2015 (month 36)? Why or why not? If you said yes, f) Do you think it would be all right to extrapolate a lot and use this model to predict the retirement account at the start of 2050 (month 480)? Why or why not? If you said yes,

3 3. We looked at the relationship between the years since 1990 (x) and a saving s account balance in dollars (y). Statcrunch gave the following exponential equation and scatterplot. Since this is a reasonably good model, let s use the equation to make some predictions. LN ( y ) = ( x ) a) What is the scope of the data (x values)? What years does the scope represent? b) Do you think the savings account balance will continue to follow this pattern into the future? Why or why not? Discuss the implications on extrapolation. How far do you think you can extrapolate before the prediction becomes really bad? Why? c) Solve the logarithmic equation to predict the savings account balance in 2006 (year 16)? d) Solve the logarithmic equation to predict the savings account balance in 2011 (year 21)? savings account in 2015 (year 25)? Why or why not? If you said yes, then go ahead and make the prediction and see if the answer looks reasonable or not. f) Do you think it would be all right to extrapolate a lot and use this model to predict the savings account in 2040 (year 50)? Why or why not? If you said yes, then go ahead and make the prediction and see if the answer looks reasonable or not.

4 4. We looked at the relationship between the metal distance in millimeters (x) and the ultrasound response values (y). Statcrunch gave the following natural log equation and scatterplot. Since this is a reasonably good model, let s use the equation to make some predictions. LN ( y ) = ( x ) a) What is the scope of the data (x values)? b) Do you think the ultrasonic response will continue to follow this pattern outside the scope of the data? Why or why not? Discuss the implications on extrapolation. How far do you think you can extrapolate before the prediction becomes really bad? Why? c) Solve the logarithmic equation to predict the ultrasonic response if the metal is 2.83 mm away? d) Solve the logarithmic equation to predict the ultrasonic response if the metal is 4.51 mm away? e) Do you think it would be all right to extrapolate some and use this model to predict ultrasonic response if the metal is 6.75 mm away? Why or why not? If you said yes,

5 5. The equations Minitab found had LOG (base 10) in them and Statcrunch had natural log (base e ) in them. Explain how this equation is actually describing an exponential function and not a Logarithmic function? What is the relationship between logarithmic functions and exponential functions? 6. Write a short paragraph discussing these examples and what you learned about the topic of reasonable verses excessive extrapolation when dealing with exponential functions.