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Average Score: 94%

A regression analysis was performed... The regression equation is y = 200.6 + 36.5x Which interpretation of this regression model is appropriate?

Rationale

An increase of 1 in the classroom size is associated with an increase in cost of $36.50.

The regression equation y = 200.6 + 36.5x indicates that for each additional unit increase in classroom size (x), the cost (y) increases by $36.50. This reflects the slope of the regression line, representing the change in the dependent variable for each unit change in the independent variable.

A (An increase of 1 in the classroom size is associated with an increase in cost of $36.50.) CORRECT

This interpretation is accurate as it correctly describes the slope of the regression equation. The coefficient of x in the equation (36.5) quantifies how much y (the cost) changes for each unit increase in x (the classroom size).

B (An increase of 1 in the classroom size is associated with an increase in cost of $200.60.) YOUR ANSWER

This choice misinterprets the regression equation. The value $200.60 is the y-intercept, representing the estimated cost when the classroom size is zero, not the change in cost per unit increase in classroom size.

C (An increase of 36.5 in the classroom size is associated with an increase in cost of $1.00.) YOUR ANSWER

This statement incorrectly reverses the relationship between classroom size and cost. It suggests a change in classroom size of 36.5 units results in only a $1.00 increase in cost, which contradicts the slope of the regression equation.

D (An increase of 200.6 in the classroom size is associated with an increase in cost of $1.00.) YOUR ANSWER

This interpretation also misrepresents the regression model. The figure $200.60 is the y-intercept and does not represent any change in classroom size; it inaccurately implies a minuscule increase in cost relative to a significant increase in classroom size.

Conclusion

The regression model provides a clear relationship between classroom size and cost, with the slope indicating that each unit increase in classroom size leads to a $36.50 increase in cost. Misinterpretations of the regression coefficients, including confusing the y-intercept with the slope, can lead to incorrect conclusions about the data's implications. Understanding these distinctions is essential for accurate analysis and application of regression results.

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