Question 1

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

The regression equation indicates that for each unit increase in classroom size (x), the cost (y) increases by $36.50, as represented by the coefficient of x in the equation.

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

This option is correct because it directly reflects the coefficient of x in the regression equation, which is 36.5. This means that for every additional unit of classroom size, the cost increases by $36.50.

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

This option is incorrect because $200.60 represents the constant term (intercept) of the regression equation, not the change in cost per unit increase in classroom size. The intercept does not indicate the change associated with the independent variable.

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

This option is incorrect as well because it misinterprets the regression coefficient. The coefficient of 36.5 indicates the increase in cost per one unit increase in classroom size, not a larger increase in classroom size leading to a $1.00 increase in cost.

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

This option is also incorrect. Similar to option C, it misrepresents the coefficients in the regression equation. The constant term does not indicate a change in cost based on increases in classroom size.

Conclusion

Option A is the only interpretation that accurately reflects the relationship defined by the regression equation, specifically the change in cost associated with a one-unit increase in classroom size. All other options either misinterpret the coefficients or incorrectly relate the variables, demonstrating a lack of understanding of regression analysis fundamentals.