2.7 Residuals

• Small residuals indicate that the regression model provides a good fit to the data.


  True
• Predicted values lie exactly on the regression line.


  True
• Residuals are the differences between the observed values of the dependent variable and the predicted values from a regression model
• Observed values are actual data points, while predicted values are estimated by the regression model
• Residuals are calculated as the difference between the observed values and the predicted values in a regression model
• What does a positive residual indicate about the observed and predicted values?

  Observed > Predicted
• What is the formula for calculating residuals in a regression model?

  Observed - Predicted Value
• The predicted value in a regression model lies exactly on the regression line.


  True
• Observed values vary around the regression line.


  True
• Large residuals suggest that the regression model adequately captures the relationship between variables.

  False
• If the observed height of a plant is 25 cm and the regression model predicts it to be 22 cm, what is the residual?

  +3 cm
• If the observed height of a plant is 22 cm and the regression model predicts it to be 25 cm, what is the residual?

  -3 cm
• Match the residual plot characteristic with its interpretation:

  Random Scatter ↔️ Regression model fits well

  Patterned Distribution ↔️ Model does not capture all relationships
• The observed value is the actual data point.
• The formula to calculate residuals is: Residual = Observed Value - Predicted Value
• A positive residual suggests that the model underestimated the actual value.
• A residual plot graphs residuals against predicted values to assess model fit.
• What are influential data points in regression analysis?

  Observations with disproportionate impact on the model
• What is the source of deviation for residuals?

  Model's inability to capture all factors
• Residuals are important because they allow us to evaluate how well the regression model fits the data
• Residuals are calculated as the difference between the observed values and the predicted values in a regression model
• An observed value is an actual data point.
• A predicted value is estimated by the regression model.
• What is the formula for calculating residuals in a regression model?

  Observed - Predicted Value
• A positive residual means the model underestimated the actual value of the data point.


  True
• A negative residual means the model overestimated the actual value of the data point.

  True
• In a good residual plot, the points are randomly scattered around zero.


  True
• If the residuals in a regression model are large, it suggests the model does not adequately capture the relationship between variables.


  True
• What are residuals in regression analysis?

  Differences between observed and predicted values
• What does a positive residual indicate?

  Observed value is greater than predicted value
• What does a negative residual suggest about the model's prediction?

  Model overestimated the actual value
• A clear pattern in a residual plot indicates the model captures all relationships.

  False
• Match the statistical concept with its definition:

  Residual ↔️ Difference between observed and predicted values

  Error ↔️ Difference between observed and true values
• What is the formula to calculate residuals?

  Residual = Observed - Predicted
• What influences observed values, and what influences predicted values in a regression model?

  All factors vs independent variables
• What is the formula to calculate residuals?

  Residual = Observed - Predicted
• A positive residual means the model underestimated the actual value.

  True
• Small residuals in a regression model indicate a good fit of the model to the data.

  True
• How are residuals calculated in a regression model?

  Observed - Predicted Value
• Match the term with its description:

  Observed Value ↔️ Actual data point

  Predicted Value ↔️ Value estimated by model