Because this approach acts as if there were a single experiment the variance that exists in the parameter estimate is larger than the variance associated with the expected value approach. The second approach to estimate the effect of a specific value of x on y treats the event as a single experiment: you choose x and multiply it times the coefficient and that provides a single estimate of y. Remember that there is a variance around the estimated parameter of x and thus each experiment will result in a bit of a different estimate of the predicted value of y. Here the question is: what is the mean impact on y that would result from multiple hypothetical experiments on y at this specific value of x. The first approach wishes to measure the expected mean value of y from a specific change in the value of x: this specific value implies the expected value. There are actually two different approaches to the issue of developing estimates of changes in the independent variable, or variables, on the dependent variable. This was why we developed confidence intervals for the mean and proportion earlier. Remember that point estimates do not carry a particular level of probability, or level of confidence, because points have no “width” above which there is an area to measure.
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