Solve the Problem $\sum ( y - \hat { y } ) ^ { 2 }$

question 56

Essay

Solve the problem.
-The sum of squares of residuals $\sum ( y - \hat { y } ) ^ { 2 }$ can be used to assess the quality of a regression model. A residual is the difference between an observed y value and the value of y predicted from the model, $\hat { y }$ . The better the model, the smaller the sum of squares of residuals. For the data below find the sum of squares of residuals which results from fitting a linear model, and the sum of squares of residuals which results from fitting a power model. Which model fits better? How can you tell?
$$\begin{array} { c | c c c c c } \mathrm { x } & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm { y } & 3 & 9 & 17 & 30 & 40\end{array}$$

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Definitions:

Variable Interval

A schedule of reinforcement where a response is rewarded after an unpredictable amount of time has passed, leading to responses at varying rates.

Avoidance Training

Avoidance training is a learning process in which an individual learns to prevent the occurrence of an unpleasant or harmful stimulus by performing a specific behavior.

Classical Conditioning

A behavior acquisition technique involving continuous pairing of two stimuli; a reaction initially triggered by the second stimulus becomes triggered by the first stimulus alone over time.

Modeling

A behavioral technique in psychology that involves learning through the observation and replication of others' behaviors.