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AP Statistics
Unit 2: Exploring Two-Variable Data
2.9 Analyzing Departures from Linearity
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Cards (27)
A linear relationship is characterized by a curved line.
False
A constant rate of change between x and y implies
linearity
.
True
What is the formula to calculate residuals?
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y_{observed} - y_{predicted}
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The key feature of linearity is that the rate of change between x and y is
constant
The defining feature of a linear relationship is a constant rate of
change
Linear relationships are characterized by a constant rate of
change
The formula for calculating residuals is
e
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e =
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y_{observed} - y_{predicted}
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, where e represents the residual
Transformations are used to linearize non-linear
relationships
Match the non-linear model type with its characteristics:
Exponential model ↔️ Models exponential growth or decay
Logarithmic model ↔️ Models relationships where y increases at a decreasing rate
What does linearity in regression refer to?
Linear relationship between x and y
What does a curved scatter plot indicate in regression analysis?
Non-linear relationship
What are the two key techniques to assess linearity visually?
Scatter plots and residual plots
Random scatter in a residual plot indicates
linearity
.
True
Linearity in regression refers to a linear relationship between the
independent variable
x and the dependent variable y.
True
Non-linearity is identified when the relationship between x and y is not constant.
True
Scatter plots are used to check for a straight-line pattern in data.
True
Residual plots display the differences between observed and
predicted
values.
True
Match the transformation type with its application:
Log transformation ↔️ When y increases at a decreasing rate
Exponential transformation ↔️ When y increases at an increasing rate
The key feature of linearity is that the rate of change between x and y is
constant
A non-linear relationship requires a more complex equation than
linear
Residual plots are created by plotting residuals against the independent
variable
Match the residual plot pattern with its interpretation:
Random scatter ↔️ Linear model is appropriate
Non-random pattern ↔️ Suggests non-linearity
Match the characteristic with its relationship type:
Straight line ↔️ Linear relationship
Curved line ↔️ Non-linear relationship
Match the pattern with its interpretation:
Curved scatter plots ↔️ Linear model is inappropriate
Systematic deviations ↔️ Non-linear model required
Match the plot type with its interpretation:
Scatter plot ↔️ Curvature indicates non-linearity
Residual plot ↔️ Non-random patterns suggest non-linearity
Match the residual plot pattern with its interpretation:
Random scatter ↔️ Linear model is appropriate
Curved pattern ↔️ Non-linear model may be suitable
Non-linear models capture relationships where the rate of change between x and y is not
constant