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23 Cards in this Set
- Front
- Back
The best fitting straight line that describes the relationship between x and y is called:
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regression line
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The equation for the regression line is called:
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The regression equation
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The regression equation is:
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ŷ = ax + b
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The regression equation algebraically describes:
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the relationship between the two variables x and y.
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The graph of the regression equation is called:
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the regression line, or line of best fit, or least-squares line.
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The regression equation expresses a relationship between:
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x and ŷ
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Requirements for finding the equation of a regression line:
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1) Sample of paired (x,y) data is a simple random sample.
2) Scatterplot confirms that points approximate a straight-line pattern. 3) Outliers are removed if they are errors. |
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Use the regression equation for predictions only if:
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1) scatterplot confirms regression line fits points well.
2) r indicates there is a strong linear correlation. 3) The prediction is not beyond the scope of the avail. sample data. |
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The best predicted value of a variable is:
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its point estimate, which is its sample mean.
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If using the regression equation to predict a value of y when given some value of x:
1) If the regression equation is a good model: 2) If the regression equation is not a good model: |
1) If the regression equation is a good model: substitute a value of x into the regression equation to find the predicted value of y.
2) If the regression equation is not a good model: the best predicted value of y is simply y̅, the mean of the y values. |
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In working with two variables related by a regression equation, the marginal change in a variable is:
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the amount that it changes when the other variable changes by exactly one unit.
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The slope in the regression equation represents the marginal change in:
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y that occurs when x changes by one unit.
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In a scatterplot, an outlier is:
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a point lying far away from the other data points.
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Paired sample data may include one or more influential points, which are:
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points that strongly affect the graph of the regression line.
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A point is an influential point if:
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the graph of the regression line changes by a considerable amount if it is graphed again with the point excluded.
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ŷ represents:
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the predicted y value
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The regression equation represents a straight line that best fits the data. The criterion to determine the line that is better than all others is based on:
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the vertical distances between the original data points and the regression line. Such distances are called residuals.
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For a pair of sample x and y values, the residual is:
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the difference between the observed sample value of y and the value of y predicted using the regression equation.
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residual =
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observed y − predicted y
y − ŷ |
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The regression equation represents the line that "best" fits the points according to:
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the least-squares property.
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A straight line satisfies the least-squares property if:
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the sum of the squares of the residuals is the smallest sum possible.
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What equation represents the least-squares property:
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∑(y − ŷ) = smallest sum possible
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Define extrapolation:
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Extrapolation is trying to predict the value of y when the value of x is out of the range of the sample x-values.
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