What is seq ss in minitab

If Minitab determines that your data include unusual observations, it identifies those observations in the Fits and Diagnostics for Unusual Observations table in the output. The observations that Minitab labels as unusual do not follow the proposed regression equation well. However, it is expected that you will have some unusual observations. The residuals versus fits graph plots the residuals on the y-axis and the fitted values on the x-axis.

Use the residuals versus fits plot to verify the assumption that the residuals are randomly distributed and have constant variance. Ideally, the points should fall randomly on both sides of 0, with no recognizable patterns in the points.

One of the points is much larger than all of the other points. Therefore, the point is an outlier. If there are too many outliers, the model may not be acceptable.

You should try to identify the cause of any outlier. Correct any data entry or measurement errors. Consider removing data values that are associated with abnormal, one-time events special causes. Then, repeat the analysis. The variance of the residuals increases with the fitted values. Notice that, as the value of the fits increases, the scatter among the residuals widens. This pattern indicates that the variances of the residuals are unequal nonconstant.

If you identify any patterns or outliers in your residual versus fits plot, consider the following solutions:. The residual versus order plot displays the residuals in the order that the data were collected. The residuals versus variables plot displays the residuals versus another variable. The variable could already be included in your model. Or, the variable may not be in the model, but you suspect it affects the response. If you see a non-random pattern in the residuals, it indicates that the variable affects the response in a systematic way.

R 2 is the percentage of variation in the response that is explained by the model. It is calculated as 1 minus the ratio of the error sum of squares which is the variation that is not explained by model to the total sum of squares which is the total variation in the model. Use R 2 to determine how well the model fits your data.

The higher the R 2 value, the better the model fits your data. R 2 always increases when you add additional predictors to a model. For example, the best five-predictor model will always have an R 2 that is at least as high the best four-predictor model. Therefore, R 2 is most useful when you compare models of the same size.

Small samples do not provide a precise estimate of the strength of the relationship between the response and predictors. If you need R 2 to be more precise, you should use a larger sample typically, 40 or more. R 2 is just one measure of how well the model fits the data. Even when a model has a high R 2 , you should check the residual plots to verify that the model meets the model assumptions. Adjusted R 2 is the percentage of the variation in the response that is explained by the model, adjusted for the number of predictors in the model relative to the number of observations.

Use adjusted R 2 when you want to compare models that have different numbers of predictors. R 2 always increases when you add a predictor to the model, even when there is no real improvement to the model.

The adjusted R 2 value incorporates the number of predictors in the model to help you choose the correct model. The first step yields a statistically significant regression model. The second step adds cooling rate to the model. Adjusted R 2 increases, which indicates that cooling rate improves the model. The third step, which adds cooking temperature to the model, increases the R 2 but not the adjusted R 2.

These results indicate that cooking temperature does not improve the model. Based on these results, you consider removing cooking temperature from the model. Predicted R 2 is calculated with a formula that is equivalent to systematically removing each observation from the data set, estimating the regression equation, and determining how well the model predicts the removed observation.

While the calculations for predicted R 2 can produce negative values, Minitab displays zero for these cases. Use predicted R 2 to determine how well your model predicts the response for new observations. Models that have larger predicted R 2 values have better predictive ability. A predicted R 2 that is substantially less than R 2 may indicate that the model is over-fit.

An over-fit model occurs when you add terms for effects that are not important in the population, although they may appear important in the sample data.

The model becomes tailored to the sample data and therefore, may not be useful for making predictions about the population. Predicted R 2 can also be more useful than adjusted R 2 for comparing models because it is calculated with observations that are not included in the model calculation. For example, an analyst at a financial consulting company develops a model to predict future market conditions.

S represents how far the data values fall from the fitted values. S is measured in the units of the response. Use S to assess how well the model describes the response. S is measured in the units of the response variable and represents the how far the data values fall from the fitted values.

The lower the value of S, the better the model describes the response. However, a low S value by itself does not indicate that the model meets the model assumptions.

You should check the residual plots to verify the assumptions. For example, you work for a potato chip company that examines the factors that affect the percentage of crumbled potato chips per container.

You reduce the model to the significant predictors, and S is calculated as 1. This result indicates that the standard deviation of the data points around the fitted values is 1.

If you are comparing models, values that are lower than 1. The standard error of the mean SE Mean estimates the variability between sample means that you would obtain if you took samples from the same population again and again. Whereas the standard error of the mean estimates the variability between samples, the standard deviation measures the variability within a single sample.

For example, you have a mean delivery time of 3. These numbers yield a standard error of the mean of 0. If you took multiple random samples of the same size, from the same population, the standard deviation of those different sample means would be around 0. Use the standard error of the mean to determine how precisely the sample mean estimates the population mean. A smaller value of the standard error of the mean indicates a more precise estimate of the population mean.

Usually, a larger standard deviation results in a larger standard error of the mean and a less precise estimate of the population mean. A larger sample size results in a smaller standard error of the mean and a more precise estimate of the population mean.

Minitab uses the standard error of the mean to calculate the confidence interval, which is a range of values likely to include the population mean. The standardized residual equals the value of a residual e i divided by an estimate of its standard deviation.

Use the standardized residuals to help you detect outliers. The observations that Minitab labels do not follow the proposed regression equation well. For more information, go to Unusual observations. Standardized residuals are useful because raw residuals might not be good indicators of outliers. The variance of each raw residual can differ by the x-values associated with it.

This unequal variation causes it to be difficult to assess the magnitudes of the raw residuals. It quantifies the variation in the data that the predictors do not explain. Seq SS Total The total sum of squares is the sum of the term sum of squares and the error sum of squares. It quantifies the total variation in the data. Interpretation Minitab uses the adjusted sums of squares to calculate the p-value for a term.

Note In an orthogonal design, the sequential sum of squares is the same as the adjusted sum of squares. Adj SS Adjusted sums of squares are measures of variation for different components of the model. Adj SS Term The adjusted sum of squares for a term is the decrease in the error sum of squares compared to a model with only the other terms. It quantifies the amount of variation in the response data that is explained by each term in the model. Adj SS Term The adjusted sum of squares for a term is the increase in the regression sum of squares compared to a model with only the other terms.

Adj SS Error The error sum of squares is the sum of the squared residuals. Adj SS Total The total sum of squares is the sum of the term sum of squares for an orthogonal design and the error sum of squares. Interpretation Minitab uses the adjusted sum of squares to calculate the p-value for a term. Adj MS 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.

Interpretation Minitab uses the adjusted mean squares to calculate the p-value for a term. F-value The Analysis of Variance table lists an F-value for each term. Interpretation Minitab uses the F-value to calculate the p-value, which you use to make a decision about the statistical significance of the terms. A sufficiently large F-value indicates that the term or model is significant. P-Value The p-value is a probability that measures the evidence against the null hypothesis. Interpretation To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis.

A significance level of 0. Frequently, a significance level of 0. It is the sum of all the adjusted sums of squares for terms in the model. Adj SS groups of terms The adjusted sum of squares for a group of terms in the model is the sum of the adjusted sum of squares for all of the terms in the group. Adj SS term The adjusted sum of squares for a term is the increase in the model sum of squares compared to a model with only the other terms. It quantifies the amount of variation in the response data that the term explains.

It quantifies the variation in the data that the model does not explain. Adj SS Total The total sum of squares is the sum of the model sum of squares and the error sum of squares. Adj MS Adjusted mean squares measure how much variation a term or a model explains, assuming that all other terms are in the model, regardless of their order in the model. F-value An F-value appears for each test in the analysis of variance table.

F-value for the model The F-value is the test statistic used to determine whether any term in the model is associated with the response. F-value for types of factor terms The F-value is the test statistic used to determine whether a group of terms is associated with the response. Examples of groups of terms are linear effects and quadratic effects. F-value for individual terms The F-value is the test statistic used to determine whether the term is associated with the response.

F-value for the lack-of-fit test The F-value is the test statistic used to determine whether the model is missing terms that include the components, process variables, and the amount in the experiment. If terms are removed from the model by a stepwise procedure, then the lack-of-fit test includes these terms also.

Interpretation Minitab uses the F-value to calculate the p-value, which you use to make a decision about the statistical significance of the test. P-value — Regression The p-value is a probability that measures the evidence against the null hypothesis. Interpretation To determine whether the model explains variation in the response, compare the p-value for the model to your significance level to assess the null hypothesis. The null hypothesis for the overall regression is that the model does not explain any of the variation in the response.

A significance level of 0. P-Value — Terms and groups of terms The p-value is a probability that measures the evidence against the null hypothesis. Interpretation If an item in the ANOVA table is statistically significant, the interpretation depends on the type of item. The interpretations are as follows: If an interaction term that includes only components is statistically significant, you can conclude that the association between the blend of components and the response is statistically significant.

If an interaction term that includes components and a process variables is statistically significant, you can conclude that the effect of the components on the response variable depends on the process variables.

If a group of terms is statistically significant, you can conclude that at least one of the terms in the group has an effect on the response. When you use statistical significance to decide which terms to keep in a model, you usually do not remove entire groups of terms at the same time. The statistical significance of individual terms can change because of the terms in the model. P-value — Lack-of-fit The p-value is a probability that measures the evidence against the null hypothesis.

Interpretation To determine whether the model correctly specifies the relationship between the response and the predictors, compare the p-value for the lack-of-fit test to your significance level to assess the null hypothesis. The null hypothesis for the lack-of-fit test is that the model correctly specifies the relationship between the response and the predictors.