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 Rยฒ value.
Rยฒ represents the percentage of variation in the response variable explained by the model. Higher Rยฒ generally indicates a better fit.
What is the exponential model formula?
ลท = abหฃ
What is the transformed exponential model formula?
ln(ลท) = ln(a) + ln(b)x
What is the power model formula?
ลท = axแต
What is the transformed power model formula?
ln(ลท) = 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 - ลท).
