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47 Cards in this Set
- Front
- Back
Response Variable (dependent variable ) |
A response variable meassures an outcome of a study. |
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Explanatory Variable (independent variables) |
An explaneatory variable may help explain or influence changes in a response variable. |
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Scatter Plot |
A scatter plot shows the relationship between two quanatative variables messured on the same indivisuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point in the graph. |
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How to make a Scatterplot by hand (three steps) |
1. Decide which variable should go on each axis. 2. Label and scale your axes. 3. Plot individual data values. |
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Dirrection |
The overall pattern moves in the same general way. |
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How to examin a Scatterplot (three steps) |
1. You can describe the overall pattern of a scatterplot by the direction, form and strength of the relationship. 2. AN important kind of departure is an outliar, an individual value that falls outside the overall pattern of the relationship. |
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Positive Association |
Two variables have a positive associaion when above- adverage values of one tend to accompany above- average values of the other and when below- adverage values also tend to occur together |
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Negetive Assosiation |
Two variables have a negetive assosiation when above- adverage values of one tend to accompany below-average values of the other. |
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Correlation r |
meassures the dirrection and strength of the linear relationship between two quantitative variables. |
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what is the sign for a positive assosiation |
r>0 |
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The sign for a negetive assosiation |
r<0 |
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Values of R near zero inidcate |
a very weak linear relationship |
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The strength of the linear relationship increases as... |
R moves away from 0 towards either 1 or -1 |
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The exstreme values of r=1 and r=-1 occur only on the case of... |
a perfect linear relationship |
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Standardized values have... |
no units |
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Correlation makes no distinction between |
expanatory and response variables |
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R does not change when we change |
units of meassurement |
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Correlation requires both variables to be... |
Quanitative |
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Use r with caution when... |
Outliars appear in the scatterplot |
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Regression line |
rehression line is a line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x |
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A regression line summarizes the reationship between two variables but only in a specific setting: |
when one of the variables helps explain or predict the other |
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Regression, unlike correlation requie that we have an... |
explanatory variable and a response variable |
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A regression line relating to y and x has an equation of the form |
Y(y hat)= a+bx |
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Y (read y hat) is the... |
predicted value of the response variable y for a given value of the expanatory variable x |
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What is b |
B is the slope the amount by which y is predicted to change when x increases by one unit |
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What is A |
A os the y intercept the predicted calue of y when x=0 |
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You cant't say how important a relationship is by : |
looking at the size of the regression line |
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The accuracy of predictions from a regression line depends on how much... |
the daa scaters about the line |
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Extapolation |
the use of a regression line for predictions far outside the interval of values if the explanatory variable x used to obtain the line. Such predictions are often not accurate. |
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We can give the equatio of the least squares regression line in terms of the BLANK and BlANK of the two variables and their correlation. |
Means and Standard Deviations |
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For an increases of one standard deviation in the value of the explanatory variabe x, the least squares regression line predicts... |
an increase of r standar deviations in the response variable Y. |
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As the correlation grows BLANK strong, the prediction Y hat moves less on response to x. |
less |
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Standardrizing a vraibale converts its mean to BLANK and its standard deviation to BLANK |
0, 1 |
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the mean of the least squares residual is always BLANK |
zero |
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residual plot |
A scatterplot of the residual against the eplanatory variable. |
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What do residual plots do ? |
Help us assess how well a regression line fits the data. |
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The residual plot should show no BLANK |
obvious pattern |
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The residuals should be BLANK |
relativly small in size |
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What does the standard deviation of residuals do ? |
Gives the appropriate size of a typica or adverage prediction error (residual) |
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SST |
measures the total variation in the y values |
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the coefficient od determination r squared in regression |
The fraction of the variation in the values of Y that is accounted for by the least squares regresssion line of Y on X |
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A and B equal the BLANK collum in calcilations. A is the Blank |
Coefficent, constant |
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The difference between BLANK and BLANK variables is important in regression. |
expanatory and response |
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Correlation and regression lines describe only BLANK relationship. |
Linear |
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Correlation and least square regression lines are not BLANK |
resistent |
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Points that are outliars in the y-dirrection of a scatter plot have BLANK |
large residuals |
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Influntial points often have BLANK residuals because they pull the regression line towards themselves |
small |