![]() ![]() ![]() So, if there is a negative error in one period, there is a greater likelihood of a negative error in the next period.Ī negative serial correlation occurs when a positive error for one observation increases the chance of a negative error for another observation. Positive serial correlation also means that a negative error for one observation increases the chance of a negative error for another observation. In other words, if there is a positive error in one period, there is a greater likelihood of a positive error in the next period as well. Positive serial correlation occurs when a positive error for one observation increases the chance of a positive error for another observation. Types of Serial Correlation Positive Serial Correlation The autocorrelation coefficient measures how closely related a series of data points are to each other. The degree of serial correlation can be measured using the autocorrelation coefficient. Similarly, if stock prices go down today, they are likely to go down tomorrow. Stock prices tend to go up and down together over time, which is said to be “serially correlated.” This means that if stock prices go up today, they will also go up tomorrow. One example of serial correlation is found in stock prices. This can happen for various reasons, including incorrect model specification, not randomly distributed data, and misspecification of the error term. In other words, it occurs when the errors in the regression are not independent of each other. QI Macros also performs Multiple Regression Analysis and Binary Logistic Regression Analysis.Serial correlation, also known as autocorrelation, occurs when the regression residuals are correlated with each other. This provides you with information on how the confidence level can impact your results, depending on where alpha is set. The 95% and 99% Confidence Levels reference when your alpha value is set at. NOTE: The straight lines found in your first chart (Salt concentration) represent the Upper and Lower Prediction Intervals, while the more curved lines are the Upper and Lower Confidence IntervalsĬonfidence Intervals provide a view into the uncertainty when estimating the mean, while Prediction Intervals account for variation in the Y values around the mean. In addition to the Summary Output above, QI Macros also calculates Residuals and Probability Data and creates scatter plots in Excel for you: Residuals Output, Probability Output and Charts For example, if the % of paved roadway = 1% the Salt concentration could be estimated as 17.547* (1%) +2.6765 = 20.2235 mg/l. Using the equation, y = Salt concentration = 2.677 + 17.547*(% paved roadway area), you could predict the salt concentration based on the percent of paved roadway. Use the Equation for Prediction and Estimation In other words, there is a relation between the two variables. Since the p value ( 0 < 0.05), we "Reject the Null Hypothesis" that the two variables are unrelated. 951 means that 95.1% of the variation in salt concentration can be explained by roadway area. Some statistics references recommend using the Adjusted R Square value. Evaluate the R Square value (0.951)Īnalysis: If R Square is greater than 0.80, as it is in this case, there is a good fit to the data. NOTE: If the first cell of your y values column is blank, that column of data will be omitted from your Regression output. QI Macros will automatically perform the regression analysis calculations for you:.Next, select your data and click on QI Macros > Statistical Tools > Regression & Other Statistics > Regression:.Enter your data into Excel with the independent variable in the left column and the dependent variable in the right column.This sample data is found in QI Macros Test Data > statistical.xlsx > Regression Data: What if we wanted to know if the salt concentration in runoff (dependent variable) is related to the percent of paved roadway area (independent variable). Regression arrives at an equation to predict performance based on each of the inputs. The purpose of regression analysis is to evaluate the effects of one or more independent variables on a single dependent variable. You Don't Have to be a Expert to Run Regression Analysis! QI Macros will do the math and analysis for you. ![]() Click on QI Macros menu > Statistical Tools > Regression.Free Agile Lean Six Sigma Trainer Training.Animated Lean Six Sigma Video Tutorials.Statistical Analysis - Hypothesis Testing. ![]()
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