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Stat 212
Exam 1 Chapter 3
22
Mathematics
Undergraduate 2
09/29/2009

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Cards

Term
Response variable
Definition
  • Dependent Variable
  • outcome variable on which comparisons are made
Term
Explanatory variable
Definition
  • Independent variable
  • defines groups to be compared to response variable in regards to values
  • ex. response / explanatory
    • Blood alcohol level/ bears consumed
    • Grade on test/ Amound of study time
    • Yield of corn per bushel / amount of rainfall
Term
Association
Definition
  • exists between 2 variables if particular value for one variable is more likely to occur with certain values of the other variable
Term
Contingency Tables
Definition
  • Display 2 categorical variables
  • Row lists categories of one variable
  • Columns list categories of other variable
  • Entires are frequencies
Term
Conditional Proportions
Definition
  • Proportions dependend on variable
    • EX. proportion of organic food w/ pesticide and proportion of conventional food w/ pesticide
Term
3 types of cases while investigating association between 2 variables
Definition
  • Both categorical (ex. food type / pesticide status)
    • Use contingency tables
  • One Quantitative / One categorical
    • Income and Gender
  • Both quantitative
Term
Constructing scatterplots
Definition
  • Horizontal axis: explanatory variable X
  • Vertical Axis: response variable Y
Term
Positively association
Definition
  • High values of X tend to occur w/ high values of Y
  • Low values of x tend to occur with low values of Y
Term
Negatively association
Definition
  • High values of one variable tend to pair w/ low vaules of the other variable
Term
Linear Correlation, r
Definition
  • Measure strength and direction o linear association btwn X and Y
    • Positive r value = positive association
    • Negative r value = negative association
    • r value close to +/- 1 = strong linear association
    • r value close to 0 = weak linear association (nonlinear relationship may exist)
Term
Properties of Correlation
Definition
  • Btwn +/- 1
    • +1 = positive linear association
    • -1 = negative linear association
  • Unit-less measure
  • 2 variables have same correlation nomatter which is treated as response variable
  • not resistant to outliers
  • does not depend on variable units
  • only measures strength of linear relationship

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Term
Quadrants
Definition
  • graph divided into 4 regions
  • Horizontal lines at mean of y
  • Vertical line at mea of x
Term
Regression line
Definition
  • Y denote response variable
  • X denote explanatory variable
  • straight line that describes how response variable changes as explanatory variable changes
  • prediction response variable given explanatory variable
Term
Residuals
Definition
  • measures size of prediction errors
  • vertical distance btwn point and regression line
  • Y- Y^       <---(y hat) 
  • Large residual = unusual observation
Term

Least Squares Method

 

Yields the regression line

Definition
  • Σ(residuals)2
  • Least squares regression line = line that minimizes vertical distance btwn points and their predictions
  • Slope = r( Sy / Sx )
  • Y-Intercept = (Average of Y) - b * (Average of X)
Term
Squared Correlation
Definition
  • Regression equation prediction better when there is a strong linear association
    • Better than using only sample mean
  • proportional reduction inerror = r2
    • Measures proportion of variation in y-values that is accounted by linear relationship of y w/ x
  • ex. correlation of 0.9 means 81% of variation in y-values cna be explained by explanatory variable
Term
Extrapolation
Definition
  • Using regression line to predict y-values for x-values outside observed range of data
Term
Regression outlier
Definition
  • Observation that lies far away from trend that rest of data follow
Term
Observation is influential if...
Definition
  • x value is relatively low/high compared to remaineder of data
  • observation is a regression outlier
  • influential observations tend to pull regression line toward that data point and away from rest.
Term
Lurkin variable
Definition
  • Unobserved variable that influences association btwn variables of primary interest
  • Not measured in study
Term
Confounding Variables
Definition
  • 2 explanatory variables both associated w/ a response variable but also associated with each other
Term
Simpson's Paradox
Definition
  • When direction of association between 2 variables changes after including 3rd variable and analyzing data at separte leves of that variable
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