If you estimate a model y=a + b * x, where the dependent variable Y is measured in billions of dollars and your predictor variable X is measured in percent then "A" represents what?
To determine the meaning of the parameter "a" in the model y = a + b * x, where the dependent variable Y is measured in billions of dollars and the predictor variable X is measured in percent, we need to understand the interpretation of the variables.
In this model, "a" represents the intercept term or the y-intercept. It indicates the expected value of the dependent variable (Y) when the predictor variable (X) is equal to zero. However, in this case, it requires further consideration since X is measured in percent.
To interpret the "a" parameter correctly, we need to convert the units of X to match with the units of Y. In this case, we can convert X from percent to its decimal form by dividing by 100. Once X is converted, "a" will represent the expected value of Y when X is equal to zero percent.
For instance, if "a" is estimated to be 2, it would imply that when the predictor variable X is zero percent, the expected value of Y would be 2 billion dollars. If X increases by 1, the expected value of Y should increase by "b" billion dollars, assuming all other factors remain constant.