All Flashcards
What is the exponential model formula?
ŷ = abˣ
What is the transformed exponential model formula?
ln(ŷ) = ln(a) + ln(b)x
What is the power model formula?
ŷ = axᵇ
What is the transformed power model formula?
ln(ŷ) = ln(a) + bln(x)
How to calculate 'a' in the original exponential model after transformation?
a = e^a* (where a* is the y-intercept of the transformed LSRL)
How to calculate 'b' in the original exponential model after transformation?
b = e^b* (where b* is the slope of the transformed LSRL)
How to calculate 'a' in the original power model after transformation?
a = e^a* (where a* is the y-intercept of the transformed LSRL)
How to calculate 'b' in the original power model after transformation?
b = b* (where b* is the slope of the transformed LSRL)
What is the definition of an outlier?
A data point with a y-value far from the regression line, resulting in a large residual.
What is the definition of a high-leverage point?
A data point with an x-value far from the other data points.
Define influential point.
A data point that significantly alters the slope, y-intercept, and/or correlation of a regression model.
What is data transformation in statistics?
The process of applying a mathematical function (e.g., logarithm) to data to achieve linearity or stabilize variance.
Define residual.
The difference between the observed y-value and the predicted y-value (y - ŷ).
Explain the impact of outliers on a regression model.
Outliers can drastically reduce the correlation and may change the y-intercept of the regression line.
Explain the impact of high-leverage points on a regression model.
High-leverage points can significantly change the slope and may change the y-intercept of the regression line.
Explain how to transform data for an exponential model.
Take the natural logarithm (ln) of the y-values to linearize the relationship between ln(y) and x.
Explain how to transform data for a power model.
Take the natural logarithm (ln) of both the x and y-values to linearize the relationship between ln(y) and ln(x).
Explain how residual plots help in assessing model fit.
A random scatter of points in the residual plot indicates a good fit. Patterns suggest the model is not appropriate.
Explain the meaning of R² value.
R² represents the percentage of variation in the response variable explained by the model. Higher R² generally indicates a better fit.