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What is multiple and partial correlation?
multiple correlation: Suppose you calculate the linear regression of a single dependent variable on more than one independent variable and that you include a mean in the linear model. The multiple correlation is analogous to the statistic that is obtainable from a linear model that includes just one independent variable. It measures the degree to which the linear model given by the linear regression is valuable as a predictor of the independent variable. For calculation details you might wish to see the wikipedia article for this statistic. partial correlation: Let's say you have a dependent variable Y and a collection of independent variables X1, X2, X3. You might for some reason be interested in the partial correlation of Y and X3. Then you would calculate the linear regression of Y on just X1 and X2. Knowing the coefficients of this linear model you would calculate the so-called residuals which would be the parts of Y unaccounted for by the model or, in other words, the differences between the Y's and the values given by b1X1 + b2X2 where b1 and b2 are the model coefficients from the regression. Now you would calculate the correlation between these residuals and the X3 values to obtain the partial correlation of X3 with Y given X1 and X2. Intuitively, we use the first regression and residual calculation to account for the explanatory power of X1 and X2. Having done that we calculate the correlation coefficient to learn whether any more explanatory power is left for X3 to 'mop up'.
When a variable is by it self do you put a one next to it?
no. It is generally known that a single variable represents 1 of that variable.
What is the difference between a variable and a algebraic expression?
A variable is a single letter that represents a number. For example x is a variable.An algebraic expression can contain variables, numbers, mathematical symbols, etcetera. An example of an algebraic expression is 3x+12.
What is the difference between a algebraic equation and a monomial?
The first is an equation which may contain any powers of the variable - including fractional powers. The second is a single term.
How do you find the probability of 2 dependent events?
That will depends entirely on how the two events are related. For instance, there may be a weak correlation, or a strong correlation, between two probabilities. You really need more information, about how the events are related. There is no single simple rule.
