A Professor of Economics Wants to Study the Relationship Between

question 106

Essay

A professor of economics wants to study the relationship between income y (in $1000s) and education x (in years). A random sample of eight individuals is taken and the results are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } \hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \\\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \\\hline\end{array}$$ Determine the coefficient of determination, and discuss what its value tells you about the two variables.

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Definitions:

Dependent Variable

The outcome factor in a study that changes in response to manipulations of the independent variable.

Predicted Score

An estimate based on a model or algorithm of what a variable's value will be based on other variables.

Regression Equation

An equation that describes the relationship between one dependent variable and one or more independent variables, often used to predict outcomes.

Regression Line

The line drawn based on values in a regression equation. Also known as a trend line.