A random pattern in a residual plot suggests the function model is a good fit.
True
A residual plot shows the differences between observed and predicted values.
True
A good residual plot has an average residual value close to zero
A small spread in a residual plot indicates the model provides consistent predictions.
True
A random pattern of residuals signals that the function model is a good fit
Discernible trends in a residual plot indicate that the model is systematically over- or under-predicting values.
True
Steps to calculate a residual
1️⃣ Obtain the actual observed value
2️⃣ Obtain the predicted value
3️⃣ Subtract the predicted value from the actual value
A random pattern in a residual plot suggests the function model is biased.
False
Steps to interpret a good residual plot
1️⃣ Check for randomness in the residuals
2️⃣ Verify that the average residual value is close to 0
3️⃣ Ensure the spread of residuals is small
A residual plot is a graphical tool used to assess the validity of a function model
A residual plot is a graphical tool used to assess the validity of a function model by showing the differences between actual observed values and predicted
What does the average value of residuals in a residual plot reveal about a model?
Bias
In a valid residual plot, the average residual value should be close to zero
Match the characteristic of a residual plot with its interpretation:
Random pattern ↔️ Model is a good fit
Curved pattern ↔️ Model is biased
Large spread ↔️ Inconsistent predictions
What is a residual plot used for?
Assess model validity
What is the purpose of a residual plot?
Assess model validity
What does an average residual value close to 0 suggest about a model?
The model is unbiased
Steps to analyze a residual plot for model validity
1️⃣ Check for a random pattern of residuals
2️⃣ Examine the average residual value
3️⃣ Assess the spread of residual values
What do individual data points with large residual values in a residual plot indicate?
Outliers
What is the formula to calculate a residual?
Actual Value - Predicted Value
The purpose of a residual plot is to assess the validity
A small spread of residuals in a residual plot shows that the model provides inconsistent predictions.
False
What does a discernible trend or shape in the residuals of a residual plot indicate about a function model?
Systematic over- or under-prediction
What is the formula for calculating a residual?
Actual Value - Predicted Value
A systematic pattern in a residual plot indicates the model fully captures the relationships in the data.
False
An invalid residual plot may show a curved pattern or clusters of residuals.
True
The residual is calculated as the actual value minus the predicted
A residual plot with an average residual value close to zero suggests the model is unbiased
What does a systematic pattern in a residual plot indicate?
Model needs revision
A small range of residual values indicates that the model provides inconsistent predictions.
False
Match the characteristic of a good residual plot with its interpretation:
Pattern ↔️ Random, no discernible pattern
Center ↔️ Average residual value near 0
Spread ↔️ Small range of residual values
A systematic pattern in a residual plot suggests the model is not fully capturing the relationships in the data
Match the key characteristic of a residual plot with its interpretation:
Pattern ↔️ Random or discernible trends
Center ↔️ Average residual value
Spread ↔️ Range of residual values
What does a systematic pattern in a residual plot indicate about the model?
Model needs revision
What does a random, unstructured pattern of residuals suggest about the model?
Model is a good fit
A random, unstructured pattern of residuals suggests the model is a good fit.
True
Steps to analyze a residual plot
1️⃣ Identify the pattern of residuals
2️⃣ Determine the average value of residuals
3️⃣ Assess the spread of residual values
What is a key characteristic of a valid residual plot in terms of pattern?
Random
What does a systematic pattern in a residual plot suggest about the model's predictions?