Explanatory (or independent) variables are variables such that changes in their value are thought to cause changes in the "dependent" variables.
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Explanatory and Response variables are just fancy words for independent and dependent variables. Explanatory is the independent variable and response is the dependent variable.
Simple regression is used when there is one independent variable. With more independent variables, multiple regression is required.
An explanatory variable is one which may be used to explain or predict changes in the values of another variable. There may be several explanatory variables.
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.
It is usually the regression coefficient: a measure of the degree to which two variables change in agreement with one another.