A Brief Version: Elementary Statistics Ch 10
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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Correlation | A statistical method used to determine whether a relationship between varibales exists.
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Regression | A statistical method used to describe the nature of the relationship between two variables; positive of negative, linear or nonlinear.
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What are the two types of relatinships that exist? | Simple Relationship and Multiple Relationship
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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.
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Multiple Relationship Analysis (Also known as Multiple Regression) | Two or more independent variables are used to predict the dependent variable.
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What are the two types of variables exist? | Independent Variable and Dependent Variable
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Independent Variable (Also called Explanatory Variable or Predictor Variable) | A variable in correlation and regression analysis that can be controlled or manipulated. (X-axis)
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Dependent Variable (Also called Response Variable) | A variable in correlation and regression analysis that cannot be controlled or manipulated. (Y-axis)
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Simple relationships can have either a: | Positive Relationship or Negative Relatinship
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Positive Realtionship | Exists when both variables increase or decrease at the same time.
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Negative Relationship | As one variable increases the other variable decreases, and vice versa.
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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.
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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.
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The range of the correlation coefficient is from: | -1 to +1
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If there is a strong positve relatinship between the variables: | The value of r will be clase to +1.
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If there is a strong negative relatinship between the variables: | The value of r will be clase to -1.
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When there is no linear relatinship between the variables or a weak relationsip: | The value of r will be clase to 0.
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What is the rounding rule for the correlation coefficient? | Round the value of r to three decimal places.
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Population Correlation Coefficient (rho) | The correlation computer by using all possible pairs of data values (x,y) taken from a population.
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Regression Line | The line of best fit of the data.
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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.
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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.
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Marginal Change | The magnitude of the change in one variable when the other variable changes exactly 1 unit.
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dengler
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