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Regression techniques are used to find the best relationship between two or more variables. Here, best is defined according to some statistical criteria. The regression line is the straight line or curve based on this relationship. The relationship need not be a straight line - it could be a curve. For example, the regression between many common variables in physics will follow the "inverse square law".
Independent variable could be the number (or spacing or size) of the laces and the dependant variable is distance. Possibly levels of the independent variable could be ranges of number of laces.
The domain. It need not be the "independent variable" since the variables could be interdependent.
The three types of variables are: Independent: it is the one that you manipulate Dependent: the one that reacts to the changes in the independent variable and is measured in a experiment Control: all the other factors that could affect the dependent variable but are kept constant through out an experiment
Usually, yes. Obviously, only if you have one: the two variables could be inter-dependent.
Regression techniques are used to find the best relationship between two or more variables. Here, best is defined according to some statistical criteria. The regression line is the straight line or curve based on this relationship. The relationship need not be a straight line - it could be a curve. For example, the regression between many common variables in physics will follow the "inverse square law".
No it doesn't. Cause and effect is not demonstrated with regression, it only shows that the variables differ together. One variable could be affecting another or the affects could be coming from the way the data is defined.
Independent variable could be the number (or spacing or size) of the laces and the dependant variable is distance. Possibly levels of the independent variable could be ranges of number of laces.
The independent variables for lava lamps could include factors like the type of wax and oil used, the temperature of the lamp, and the size and shape of the glass container. These variables can be manipulated or controlled to observe their effects on the behavior and appearance of the lava lamp.
Some independent variables for a balloon-powered car experiment could include the size of the balloon, the amount of air blown into the balloon, the weight of the car, and the surface the car is tested on. These variables can be changed or controlled by the experimenter to observe their effects on the car's performance.
Examples of independent variables include age, gender, temperature, amount of sunlight, type of treatment administered, and level of education. These variables are manipulated or selected by the researcher to observe their effect on the dependent variable in an experiment.
Although not everyone follows this naming convention, multiple regression typically refers to regression models with a single dependent variable and two or more predictor variables. In multivariate regression, by contrast, there are multiple dependent variables, and any number of predictors. Using this naming convention, some people further distinguish "multivariate multiple regression," a term which makes explicit that there are two or more dependent variables as well as two or more independent variables.In short, multiple regression is by far the more familiar form, although logically and computationally the two forms are extremely similar.Multivariate regression is most useful for more special problems such as compound tests of coefficients. For example, you might want to know if SAT scores have the same predictive power for a student's grades in the second semester of college as they do in the first. One option would be to run two separate simple regressions and eyeball the results to see if the coefficients look similar. But if you want a formal probability test of whether the relationship differs, you could run it instead as a multivariate regression analysis. The coefficient estimates will be the same, but you will be able to directly test for their equality or other properties of interest.In practical terms, the way you produce a multivariate analysis using statistical software is always at least a little different from multiple regression. In some packages you can use the same commands for both but with different options; but in a number of packages you use completely different commands to obtain a multivariate analysis.A final note is that the term "multivariate regression" is sometimes confused with nonlinear regression; in other words, the regression flavors besides Ordinary Least Squares (OLS) linear regression. Those forms are more accurately called nonlinear or generalized linear models because there is nothing distinctively "multivariate" about them in the sense described above. Some of them have commonly used multivariate forms, too, but these are often called "multinomial" regressions in the case of models for categorical dependent variables.
The domain. It need not be the "independent variable" since the variables could be interdependent.
The three types of variables are: Independent: it is the one that you manipulate Dependent: the one that reacts to the changes in the independent variable and is measured in a experiment Control: all the other factors that could affect the dependent variable but are kept constant through out an experiment
The independent variables in an ice melting experiment could include factors that might affect the rate of ice melting, such as temperature, surface area of the ice cube, presence of salt or other substances on the ice, or the ambient humidity. These are variables that can be manipulated by the researcher to observe their impact on the melting process.
Usually, yes. Obviously, only if you have one: the two variables could be inter-dependent.
There are many cases where you won't get useful results from regression. The two most common kinds of issues are (1) when your data contain major violations of regression assumptions and (2) when you don't have enough data (or of the right kinds). Core assumptions behind regression include - That there is in fact a relationship between the outcome variable and the predictor variables. - That observations are independent. - That the residuals are normally distributed and independent of the values of variables in the model. - That each predictor variable is not a linear combination of any others and is not extremely correlated with any others. - Additional assumptions depend on the nature of your dependent variable; for example whether it is measured on a continuous scale or is categorical yes/no etc. The form of regression you use (linear, logistic, etc.) must match the type of data. Not having enough data means having very few cases at all or having large amounts of missing values for the variables you want to analyze. If you don't have enough observations, your model either will not be able to run or else the estimates could be so imprecise (with large standard errors) that they aren't useful. A generic rule some people cite is that you need 10-20 cases per variable in the model; there's nothing magic about that number and you might get by just fine with less, but it suggests you could run into trouble if you have much less that that. Missing values can be a big problem as well and in the worst case could skew your results if they are not handled properly.