If $f$ Is a Function Of $x$ And $y$ , And $y$ Is a Function Of

question 51

Essay

If $f$ is a function of $x$ and $y$ , and $y$ is a function of $x$ , then indirectly $f$ depends only on $x$ : $g ( x ) = f ( x , y ( x ) )$ . Use the Chain Rule to write an expression for $\frac { d g } { d x }$ in terms of $\frac { \delta f } { \delta x }$ and $\frac { \delta f } { \delta y }$ .

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Definitions:

Regression Analysis

An approach in statistics for modeling how a dependent variable is related to one or more independent variables.

Dependent Variable

The variable in an experiment that is expected to change as a result of manipulations to the independent variable.

Residual

The difference between observed and predicted values in a regression analysis.

Regression Source Table

A tabular representation in regression analysis that summarizes the sources of variation in the data, including measures like the sum of squares due to regression and residual error.