calculate unknown from linear regression equation

Unlike the adjusted sums of squares, the sequential sums of squares depend on the order the terms are entered into the model. Sequential sums of squares are measures of variation for different components of the model. The more DF for pure error, the greater the power of the lack-of-fit test.

The lack-of-fit test uses the degrees of freedom for lack-of-fit. The DF for lack-of-fit allow a test of whether the model form is adequate. If the two conditions are met, then the two parts of the DF for error are lack-of-fit and pure error. For example, if you have 3 observations where pressure is 5 and temperature is 25, then those 3 observations are replicates. Replicates are observations where each predictor has the same value. The second condition is that the data contain replicates. 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. For example, if you have a continuous predictor with 3 or more distinct values, you can estimate a quadratic term for that predictor. The first condition is that there must be terms you can fit with the data that are not included in the current model. If two conditions are met, then Minitab partitions the DF for error. Increasing the number of terms in your model uses more information, which decreases the DF available to estimate the variability of the parameter estimates. Increasing your sample size provides more information about the population, which increases the total DF. The DF for a term show how much information that term uses.

The total DF is determined by the number of observations in your sample. The analysis uses that information to estimate the values of unknown population parameters. The total degrees of freedom (DF) are the amount of information in your data.

Calculate unknown from linear regression equation