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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 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)
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).