Module 4 Data Analysis Guide using Minitab
Non-linear v. Linear:

Transform from nonlinear to linear – Tukey Transformation (makes Minitab easy)
Scatterplot:
Create a scatterplot of your data. Determine what models you could potentially use to describe the correlation or
relationship between your quantitative variables.

Minitab: Graph  Scatterplot  Simple Graph
Linear Model (Graph with Linear Model, Residual Plot, r-value):


Graph and Residual Plot
o Minitab: Stat  Regression  Fitted Line Plot
 Select your Response(y) and Predictor(explanatory x) Variables
 Select Linear as the Type of Regression Model
 Under the Graph Option  Residuals versus the variables (at bottom): Select your
Explanatory(x) Variable
r-value
o Minitab: Stat  Basic Statistics  Correlation
 Input or select both of the variables (Explanatory and Response: The order you input them does
not matter for this part)
Quadratic Model (Graph/Residual Plot based on a Quadratic Model)

Graph and Residual Plot
o Minitab: Stat  Regression  Fitted Line Plot
 Select your Response(y) and Predictor(explanatory x) Variables
 Select Quadratic as the Type of Regression Model
 Under the Graph Option  Residuals versus the variables (at bottom): Select your
Explanatory(x) Variable
*When using the following exponential or logarithmic models it is highly recommended to close minitab and start
fresh.
Exponential (Growth / Decay) Model: (Graph/Residual Plot based on an Exponential Model)

Graph and Residual Plot
o Minitab: Stat  Regression  Fitted Line Plot
 Select your Response(y) and Predictor(explanatory x) Variables
 Select Linear as the Type of Regression Model
 Depending on whether it is a Growth OR Decay you will need to select an Option (refer
to your Tukey Transformation Circle):
o For Growth: Options  Select Log 10 of Y
o For Decay: Options  Select Log 10 of X
 Under the Graph Option  Residuals versus the variables (at bottom): Select your
Explanatory(x) Variable
Logarithmic (Growth / Decay) Model: (Graph/Residual Plot based on an Exponential Model)

Graph and Residual Plot
o Minitab: Stat  Regression  Fitted Line Plot
 Select your Response(y) and Predictor(explanatory x) Variables
 Select Linear as the Type of Regression Model
 We have to select the Log 10 of X Option to transform the linear model into a
logarithmic model (refer to your Tukey Transformation Circle):
o Options  Select Log 10 of X
 Under the Graph Option  Residuals versus the variables (at bottom): Select your
Explanatory(x) Variable
Organize your analysis by filling in the table below:
Model
Residual Plot
(vs. x-values or Versus Fit)
[What do you see? Describe the
shape: oval, band, fan, U-shape, Sshape, etc.]
r2
se
Linear
Exponential (growth)
Exponential (decay)
Quadratic
Logarithmic
Does
not
apply
Recall some of the analysis components we have used in modules 3 & 4
Linear:
a) r-value: Tells us the direction and strength of the linear association between two quantitative variables
b) Slope (m): This gives the average rate of change of the response(y) variable with respect to the explanatory(x)
variable. We interpret this expression as: “For every one unit increase in the explanatory variable, there is a
predicted __”m”__ increase/decrease in the response variable on average.” Note, we interpret the slope
from viewing the slope, m, as
𝒎
𝟏
and don’t forget to include the appropriate units in your interpretation.
c) Y-Intercept: This is a point with coordinates (0,b). We interpret this to mean: “When the explanatory
variable is zero the predicted response variable is b units.” Note: Don’t forget to include the appropriate
units in your interpretation and whether it has meaning in context. Remember that the y-intercept is not a
rate of change like the slope.
Residual Plots:
d) When analyzing residual plots, you want to give a description of the shape or what you see. If the data is very
scattered, we may use descriptions like band or oval shaped. If there is a pattern to the data, we use
descriptions such as U-shaped, downward U-shaped, S-shaped, pipe shaped, wave, side by side parabolas, etc.
In general, the less of a pattern or more spread out and closer to zero the residual plot is, the better the fit.
Also, the more crossing the pattern looks the better. So a residual plot with an S-shape would be a better fit
than a residual plot with a U-shape assuming they were somewhat equivalent in their distance from zero.
Linear / Non-Linear:
e) Coefficient of Determination (r2): This value is interpreted as a percentage. It measures the percent of
variation in the response variable that is explained by its linear/quadratic/exponential/logarithmic
relationship with the explanatory. We interpreted this measurement as: “The explanatory variable explains
or accounts for r2 % of the total variation in the response variable when using the _________ model. This
means that (1-r2) % of the total variation remains unexplained or unaccounted for when using this model.
f)
Standard Error of Regression (Se): This value gives us an estimation of the average error in our predictions of
the response variable when using the ________________ model. We interpreted this measurement as: “On
average, we estimate that our predictions will be off by +/- __Se__ units.” Note: Make sure to use the units
of your response variable.