## Chapter 3 Examining Relationships

##### Created by:

rocknrabbi  on October 27, 2010

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# Chapter 3 Examining Relationships

 Response Variablesmeasures the outcome of the study
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#### Definitions

Response Variables measures the outcome of the study
Coefficient of Determinent the proportion of the total sample variablility that is explained by the least-squares regression of y on x
Residuals the differences between data values and the corresponding values predicted by the regression model;residual= observed y - predicted y
Residual Plot a scatteplot of the regression residuals against the explanatory variable; helps to assess the fit of the regression line
Linear when points of data lie in a straight-line pattern on a graph
Explanatory Variable attempts to explain the observed outcomes of a study
Independent Variable variable that is changed in an experiment
Dependent Variable variable that changes as a result of a change in the independent variable
Scatter Plot a graphed cluster of dots, each of which represents the values of two variables. The slope of the points suggests the direction of the relationship between the two variables. The amount of scatter suggests the strength of the correlation.
r2 the fraction of te variation in the values of y thatis explained by least-squares regression of y on x
SSM sum of squares of deviations about the mean y hat and the sum of squares of deviations about the regression line y hat would be approximately the same
SSE sum of the squares for errors: sum (y-y)^2
Regression Line a straight line that describes how a response variable y changes as an explanatory variable x changes
Mathematical Model one or more equations that represent the way a system or process works
Least-square Regression Line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible
Positively Associated when above average values of one tend to accompany above-average values of the other and below average values also tend to occur together
Negatively Association when above average values of one tend to accompany below-average values of the other, and vice versa
Correlation measures the strength and direction of the linear relationship between two quatitative variable
r-Value written in place of correaltion
Influential Observation a data point that would significantly change the correlation or least-squares regression line of a given distribution if removed

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