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Multiple regression analysis examines the relationship of several dependent variables on the independent variable?
True.
How do you explain the analysis of variance assuming that your audience has not had a statistic class before?
The measurement of any statistical variable will vary from one observation to another. Some of this variation is systematic - due to variations in some other variable that "explains" these variations. There may be several such explanatory variables - acting in isolation or in conjunction with one another. Finally, there will be a residual variation which cannot be explained by any of these "explanatory" variables. The statistical technique called analysis of variance first calculates the total variation in the observations. The next step is to calculate what proportion of that variation can be "explained" by other variables, and finding the residual variation. A comparison of the explained variation with the residual variation is an indicator of whether or not the amount explained is statistically significant. The word "explain" is in quotes because there is not always a causal relationship. The causality may go in the opposite direction. Or the variables may be related to another variable that is not part of the analysis.
Is there one dependent variable in an experiment?
No, there can be several outputs that are dependent variables. For example, you will have a number of grades in different subjects when you finish school. So the experiment (your schooling) will result in a number of dependent variables. Similarly, the school's outcome for its "experiment" of teaching a number of pupils will be several sets exam grades: a different dependent variable for each subject.
How are polynomials used in science?
In solving multi variable equations such as in the analysis of MRI or CAT scan data. Several thousand equations in several thousand variables are utilized, impossible without a computer.
What should be the only independent variable?
In most real life cases, limiting an experiment to only one independent variable makes the whole experiment a waste of time. More often than not there are several independent variables.
