Final answer:
A coefficient of determination of 0.91 signifies that 91 percent of the variation in the dependent variable can be explained by the independent variable, indicating a strong relationship but not necessarily significance or the direction of the relationship.
Step-by-step explanation:
A coefficient of determination of 0.91 means that 91 percent of the variation in the dependent variable (cost) can be explained by the variation in the independent variable. This value, also known as r², is the square of the correlation coefficient r. If r is positive, as one variable increases, so does the other; if r is negative, the variables move in opposite directions. A coefficient of determination close to 1 signifies a strong relationship between the variables.
The interpretation of the coefficient of determination does not mean that the variables move together in the same direction - this is a characteristic of the correlation coefficient r itself. It also does not mean the model is significant 91 percent of the time; rather, significance is determined through hypothesis testing.
Finally, a higher coefficient of determination does not directly imply that the parameter is not significant. Statistical significance is typically assessed with a p-value or similar statistical test, and is not directly related to the value of r².