True or False. A data set resulted in a regression equation of Y = 17.08 - 1.16x From the equation we can determine that the X variable is directly related to the Y variable.
True. From the given regression equation, Y = 17.08 - 1.16x, we can determine that the X variable is directly related to the Y variable.
To understand why, let's break down the equation.
In a regression equation, Y represents the dependent variable and X represents the independent variable. The equation states that Y can be determined by taking the constant term (17.08) and subtracting a multiple of X (1.16x) from it.
When the coefficient of X (1.16) is negative, as it is in this case, it indicates an inverse relationship between X and Y. This means that as the value of X increases, the value of Y will decrease. In other words, the two variables move in opposite directions.
For example, if X were to increase by 1 unit, the predicted value of Y would decrease by 1.16 units. If X were to decrease by 1 unit, the predicted value of Y would increase by 1.16 units.
Overall, this indicates that the X variable is negatively or inversely related to the Y variable in this regression equation, and not directly related.