High Score the Longer You Play a Video Game, the Higher

question 107

Essay

High Score The longer you play a video game, the higher score you can usually achieve.
An analysis of a popular game found the following relationship between the hours a
player has played a game and their corresponding high score on that game. Dependent variable is High Score
R-squared $= 76.5 \%$
$s = 383.3$ with 89 degrees of freedom
$\begin{array} { l c c } \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } \\ \text { Constant } & 524.8 & 145.3 \\ \text { Hours } & 2498.8 & 324.5 \end{array}$
a. Write the regression equation and define the variables of your equation in context.
b. Interpret the slope in context.
c. Interpret the y-intercept in context.
d. Interpret s in context.
e. What is the correlation coefficient? Interpret this value in context.

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Definitions:

Marginal Product

The increase in output that results from adding one more unit of a specific input, holding all other inputs constant.

Total Product

The total output or production achieved by a firm from a given amount of inputs.

Marginal Product

The additional output produced when one additional unit of an input is employed, with all other factors remaining constant.

Total Product

The total output of goods and services produced by a firm during a specific period.