2.9 Analyzing Departures from Linearity

• 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?

  $e =$$y_{observed} - y_{predicted}$
• The key feature of linearity is that the rate of change between x and y is constant
• The defining feature of a linear relationship is a constant rate of change
• Linear relationships are characterized by a constant rate of change
• The formula for calculating residuals is $e =$$y_{observed} - y_{predicted}$, 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