All Flashcards
What are the differences between a good residual plot and a bad residual plot?
Good: Random scatter, no pattern | Bad: Clear pattern (curve, funnel), indicates non-linearity.
What are the differences between a positive residual and a negative residual?
Positive: Model underestimated, y > ŷ | Negative: Model overestimated, y < ŷ
What are the key differences between a scatterplot and a residual plot?
Scatterplot: Shows relationship between x and y | Residual Plot: Shows residuals (y-ŷ) against x, assessing model fit.
Compare the implications of residuals clustered near zero versus residuals spread far from zero.
Near Zero: Model predictions are close to actual values, better fit | Far From Zero: Model predictions are less accurate, poorer fit.
What are the differences between using a linear model and a non-linear model based on residual plots?
Linear Model: Appropriate when residuals are randomly scattered | Non-Linear Model: More appropriate when residuals show a pattern.
What is the definition of a residual?
The difference between the observed value (y) and the predicted value (ŷ).
What is the definition of a residual plot?
A scatterplot of the residuals (y - ŷ) against the predictor variable (x).
Define a positive residual.
The model underestimated the true value; actual value is higher than predicted.
Define a negative residual.
The model overestimated the true value; actual value is lower than predicted.
What does a random scatter of residuals indicate?
A linear model is appropriate.
What is the formula for calculating a residual?
What is the goal of a linear regression model in terms of residuals?
Minimize the sum of the squared residuals (least squares criterion).
How do you calculate the predicted value (ŷ) using the Least Squares Regression Line (LSRL)?
Using the equation of the LSRL: ŷ = a + bx, where a is the y-intercept and b is the slope.
Given the LSRL and a data point (x, y), how do you calculate the residual?
- Find the predicted value (ŷ) using the LSRL. 2. Subtract the predicted value from the actual value (y): Residual = y - ŷ.
What does a residual of 0 indicate?
The model perfectly predicted the observed value.