![]() ![]() If you need your calculation of r2 to be "rigorously defensible" (for a publication maybe), then I might suggest cross checking Excel's calculation with a dedicated statistics package. Perhaps further search of the kowledgebase will yield additional discussion that either validates the algorithms MS uses, and/or shows where they are still weak. I would invite further research into this. If the two regression tools are giving different results, then there is obviously still some kind of problem in Excel. ![]() Microsoft has not always been careful or thorough in how they program some of these statistical functions (maybe they are too busy designing "ribbons" and other fluff for Excel).Īs noted in the link, MS made changes for 2003 (your profile indicates 2003), so the algorithms may be better than what I have. ![]() I know that a lot of hardcore statisticians say, "Friends don't let friends use Excel for statistics" and I believe this is part of the reason. It's long and detailed, but this is one of MS's discussions of the issue One of the big problems is that it calculated r^2 incorrectly, especially for regressions where the constant is forced to be 0. The model is designed to estimate the effects of independent variables on some dependent variable in accordance with a proposed theory.I don't know all of the details, but I know that one of the criticisms of Excel (especially prior to 2003) involved the algorithms for the LINEST()/regression functions. The independent variables are independent of \(Y\), but are also assumed to be independent of the other \(X\) variables.First, plot data for Metal A only as an XY Scatter plot (the same way you did with the data in Part A). Again, remember to enter the x values to the left of the y values. Be sure to label your data columns A and B. This can be seen in Figure 13.6 by the shape of the distributions placed on the predicted line at the expected value of the relevant value of \(Y\). Enter this new data on a new worksheet (Sheet 2) in Excel. ![]() While the independent variables are all fixed values they are from a probability distribution that is normally distributed.Figure 13.6 shows the case of homoscedasticity where all three distributions have the same variance around the predicted value of \(Y\) regardless of the magnitude of \(X\). If the assumption fails, then it is called heteroscedasticity. The assumption is for constant variance with respect to the magnitude of the independent variable called homoscedasticity. It is plausible that as income increases the variation around the amount purchased will also increase simply because of the flexibility provided with higher levels of income. Consider the relationship between personal income and the quantity of a good purchased as an example of a case where the variance is dependent upon the value of the independent variable, income. The meaning of this is that the variances of the independent variables are independent of the value of the variable. The error term is a random variable with a mean of zero and a constant variance.This assumption is saying in effect that \(Y\) is deterministic, the result of a fixed component “\(X\)” and a random error component “\(\epsilon\).” The independent variables, \(x_i\), are all measured without error, and are fixed numbers that are independent of the error term.Some of the failures of these assumptions can be fixed while others result in estimates that quite simply provide no insight into the questions the model is trying to answer or worse, give biased estimates. If one of these assumptions fails to be true, then it will have an effect on the quality of the estimates. These are that the \(Y\) is normally distributed, the errors are also normally distributed with a mean of zero and a constant standard deviation, and that the error terms are independent of the size of \(X\) and independent of each other.Īssumptions of the Ordinary Least Squares Regression ModelĮach of these assumptions needs a bit more explanation. \nonumber\]Īs with our earlier work with probability distributions, this model works only if certain assumptions hold. ![]()
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