The total degrees of freedom (DF) are the amount of information in your data. The analysis uses that information to estimate the values of unknown population parameters. The total DF is determined by the number of observations in your sample. The DF for a term show how much information that term uses. Increasing your sample size provides more information about the population, which increases the total DF. Increasing the number of terms in your model uses more information, which decreases the DF available to estimate the variability of the parameter estimates.
If two conditions are met, then Minitab partitions the DF for error. The first condition is that there must be terms you can fit with the data that are not included in the current model. For example, if you have a continuous predictor with 3 or more distinct values, you can estimate a quadratic term for that predictor. If the model does not include the quadratic term, then a term that the data can fit is not included in the model and this condition is met.
The second condition is that the data contain replicates. Replicates are observations where each predictor has the same value. For example, if you have 3 observations where pressure is 5 and temperature is 25, then those 3 observations are replicates.
If the two conditions are met, then the two parts of the DF for error are lack-of-fit and pure error. The DF for lack-of-fit allow a test of whether the model form is adequate. The lack-of-fit test uses the degrees of freedom for lack-of-fit. The more DF for pure error, the greater the power of the lack-of-fit test.
Sequential sums of squares are measures of variation for different components of the model. Unlike the adjusted sums of squares, the sequential sums of squares depend on the order the terms are entered into the model. In the Analysis of Variance table, Minitab separates the sequential sums of squares into different components that describe the variation due to different sources.
Adjusted sums of squares are measures of variation for different components of the model. The order of the predictors in the model does not affect the calculation of the adjusted sums of squares. In the Analysis of Variance table, Minitab separates the sums of squares into different components that describe the variation due to different sources.
Minitab uses the adjusted sums of squares to calculate the p-value for a term. Minitab also uses the sums of squares to calculate the R^{2} statistic. Usually, you interpret the p-values and the R^{2} statistic instead of the sums of squares.
Adjusted mean squares measure how much variation a term or a model explains, assuming that all other terms are in the model, regardless of the order they were entered. Unlike the adjusted sums of squares, the adjusted mean squares consider the degrees of freedom.
The adjusted mean square of the error (also called MSE or s^{2}) is the variance around the fitted values.
Minitab uses the adjusted mean squares to calculate the p-value for a term. Minitab also uses the adjusted mean squares to calculate the adjusted R^{2} statistic. Usually, you interpret the p-values and the adjusted R^{2} statistic instead of the adjusted mean squares.
Minitab uses the F-value to calculate the p-value, which you use to make a decision about the statistical significance of the terms and model. The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
A sufficiently large F-value indicates that the term or model is significant.
If you want to use the F-value to determine whether to reject the null hypothesis, compare the F-value to your critical value. You can calculate the critical value in Minitab or find the critical value from an F-distribution table in most statistics books. For more information on using Minitab to calculate the critical value, go to Using the inverse cumulative distribution function (ICDF) and click "Use the ICDF to calculate critical values".
The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis. Minitab automatically performs the pure error lack-of-fit test when your data contain replicates, which are multiple observations with identical x-values. Replicates represent "pure error" because only random variation can cause differences between the observed response values.
If the p-value is larger than the significance level, the test does not detect any lack-of-fit.