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# Elem Stats ch 10

### A Brief Version: Elementary Statistics Ch 10

Correlation A statistical method used to determine whether a relationship between varibales exists.
Regression A statistical method used to describe the nature of the relationship between two variables; positive of negative, linear or nonlinear.
What are the two types of relatinships that exist? Simple Relationship and Multiple Relationship
Simple Relationship Analysis (Also known as Simple Regression) A relationship in which only two variables are under study, there is one independent variable that is used to predict the dependent variable.
Multiple Relationship Analysis (Also known as Multiple Regression) Two or more independent variables are used to predict the dependent variable.
What are the two types of variables exist? Independent Variable and Dependent Variable
Independent Variable (Also called Explanatory Variable or Predictor Variable) A variable in correlation and regression analysis that can be controlled or manipulated. (X-axis)
Dependent Variable (Also called Response Variable) A variable in correlation and regression analysis that cannot be controlled or manipulated. (Y-axis)
Simple relationships can have either a: Positive Relationship or Negative Relatinship
Positive Realtionship Exists when both variables increase or decrease at the same time.
Negative Relationship As one variable increases the other variable decreases, and vice versa.
Scatter Plot A graph of the ordered pairs (x,y) of the numbers consisting of the independent variable x and the independent varibale x and teh dependent variable y.
Correlation Coefficient Computed from the sample data measures the strength and direction of a limear relationship between two variables. The symbol for the sample correlation coefficient is r. The symbol for the population correlation coeficient is the Greek letter rho - p.
The range of the correlation coefficient is from: -1 to +1
If there is a strong positve relatinship between the variables: The value of r will be clase to +1.
If there is a strong negative relatinship between the variables: The value of r will be clase to -1.
When there is no linear relatinship between the variables or a weak relationsip: The value of r will be clase to 0.
What is the rounding rule for the correlation coefficient? Round the value of r to three decimal places.
Population Correlation Coefficient (rho) The correlation computer by using all possible pairs of data values (x,y) taken from a population.
Regression Line The line of best fit of the data.
Line of Best Fit The sum of the squares of the vertical distances from each point to the line is at a mininum. The values of y will be predicted from the values of x, so the closer the point are to the line the better the fit and the prediction will be.
What are the assumptions for a valid predictions in regression? For any specific value of the independent variable x, the value of the dependent variable y must be normally distributed about the regression line. The standard deviation of must be the same for each of the dependent varibales and independent variables.
Marginal Change The magnitude of the change in one variable when the other variable changes exactly 1 unit.
Created by: dengler