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)
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.
What are the differences between outliers and high-leverage points?
Outliers: y-value far from the regression line, large residual | High-Leverage Points: x-value far from other points, potentially changes slope.
What are the differences between exponential and power model transformations?
Exponential: ln(y) vs. x | Power: ln(y) vs. ln(x)
What are the differences between the effects of outliers vs high leverage points?
Outliers: Affect correlation and y-intercept more | High Leverage Points: Affect the slope more
What are the differences between interpreting 'b' in transformed exponential and power models?
Exponential: b* needs to be exponentiated (e^b*) to find original 'b' | Power: b* is the original 'b'
What are the differences between the original exponential and power models?
Exponential: ŷ = abˣ (y changes exponentially with x) | Power: ŷ = axᵇ (y changes by a power of x)