Nonlinear Regression Act3
Exponential Regression Criteria
Directions: In this activity we will be exploring the Residual plots for Exponential functions with
Statcrunch or Minitab. We will then check the regression criteria below.
For StatCrunch, go to the Stat menu, click on “regression”, then “simple linear”. Put in the x and y
variables. Under the “transformation” section click on “Natural Logarithm: log(y)”. Make sure to click
on fitted line plot for the scatterplot, Histogram of the Residuals and the Residuals vs the x values.
Keep in mind that even though the formula says “log” it is actually natural log (LN).
For Minitab, you will need to go to the “Statistics” menu in Minitab. Then click on “regression” and
then fitted line plot. Make sure to click on “log y” under the options button. Under the graphs
button, click on “Histogram of Residuals” and in the open box at the bottom put in the x variable. This
will give you the residual plot vs the x variable. Keep in mind that Minitab numbers will be different
from Statcrunch. Minitab is using Log base 10.
Criteria for Nonlinear Regression
A. Two quantitative variables. (The data needs to be quantitative ordered pair data.)
B. No Influential Outliers. (Remember outliers drastically effect correlation. One point can make all
the difference.)
C. Scatterplot has the curved pattern you are exploring. (For these problems, does the scatterplot
show an exponential growth or exponential decay pattern? Does the residual plot not show a different
nonlinear curve that would be better?)
D. Constant Standard Deviation Condition is satisfied. (This is often called Homoskedasticity. We
basically don’t want a fan shape in our residual plot. We want the dots to be spaced consistently from
the regression line.)
E. Histogram of Residuals is close to bell shaped (nearly normal).
F. Histogram of Residuals has a center close to zero. (The highest hill should be close to zero.)
Note: The more of these criteria a regression curve satisfies, the better the nonlinear relationship and
the more accurate our predictions will be.
1. Open the Module 4 Data Sets in Excel. Copy and paste the years since 1995 and wind power
into Statcrunch or Minitab. This data gives the number of years since 1995 and the world wide
wind power capacity in MW (megawatts).
a) Let the number of years by the explanatory variable and the wind power be the
response variable. Use Statcrunch or Minitab to make a scatter plot of the ordered pairs
with the exponential curve. You will also need the Histogram of the Residuals and the
Residual plot vs the x values. You will also need the r-squared value and the equation of
the curve.
b) Use the scatterplot, R-squared, Histogram of Residuals and the residual plot to check
the regression criteria A through F above. Write a paragraph explaining your findings.
c) Save your scatterplot with exponential function, residual plots, and paragraph on your
flash drive.
2. Open the Module 4 Data Sets in Excel. Copy and paste the month and retirement account
balance into Statcrunch or Minitab. The following data gives the balance in a retirement
account. The couple started with $78,000 in their account in 2010, and have been slowly
making withdrawals for their living expenses. The data gives the months since January 2010 and
the retirement account balance in thousands of dollars.
a) Let the months be the explanatory variable and the retirement account balance be the
response variable. Use Statcrunch or Minitab to make a scatter plot of the ordered pairs
with the exponential curve. You will also need the Histogram of the Residuals and the
Residual plot vs the x values. You will also need the r-squared value and the equation of
the curve.
b) Use the scatterplot, R-squared, Histogram of Residuals and the residual plot to check
the regression criteria A through F above. Write a paragraph explaining your findings.
c) Save your scatterplot with exponential function, residual plots, and paragraph on your
flash drive.
3. Open the Module 4 Data Sets in Excel. Copy and paste the years since 1990 and the saving’s
account balance into Statcrunch or Minitab. The savings account was opened in 1990. The
following ordered pairs give the number of years since 1990 and the amount of money in a
savings account.
a) Let the years be the explanatory variable and the saving account balance be the
response variable. Use Statcrunch or Minitab to make a scatter plot of the ordered pairs
with the exponential curve. You will also need the Histogram of the Residuals and the
Residual plot vs the x values. You will also need the r-squared value and the equation of
the curve.
b) Use the scatterplot, R-squared, Histogram of Residuals and the residual plot to check
the regression criteria A through F above. Write a paragraph explaining your findings.
c) Save your scatterplot with exponential function, residual plots, and paragraph on your
flash drive.
4. Open the Module 4 Data Sets in Excel. Copy and paste the metal distance and ultrasound
response into Statcrunch or Minitab. Ultrasound is used in a variety of applications.
a) Let the explanatory variable be the metal distance in millimeters and the response
variable be the ultrasound response. Use Statcrunch or Minitab to make a scatter plot
of the ordered pairs with the exponential curve. You will also need the Histogram of the
Residuals and the Residual plot vs the x values. You will also need the r-squared value
and the equation of the curve.
b) Use the scatterplot, R-squared, Histogram of Residuals and the residual plot to check
the regression criteria A through F above. Write a paragraph explaining your findings.
c) Save your scatterplot with exponential function, residual plots, and paragraph on your
flash drive.
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