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# Elem Stats ch 10

### A Brief Version: Elementary Statistics Ch 10

Question | Answer |
---|---|

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