• Dependent Variable
• outcome variable on which comparisons are made

• 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

• exists between 2 variables if particular value for one variable is more likely to occur with certain values of the other variable

• Display 2 categorical variables
• Row lists categories of one variable
• Columns list categories of other variable
• Entires are frequencies

• Proportions dependend on variable
  • EX. proportion of organic food w/ pesticide and proportion of conventional food w/ pesticide

• Both categorical (ex. food type / pesticide status)
  • Use contingency tables
• One Quantitative / One categorical
  • Income and Gender
• Both quantitative

• Horizontal axis: explanatory variable X
• Vertical Axis: response variable Y

• High values of X tend to occur w/ high values of Y
• Low values of x tend to occur with low values of Y

• High values of one variable tend to pair w/ low vaules of the other variable

• 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)

• 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

[image]

• graph divided into 4 regions
• Horizontal lines at mean of y
• Vertical line at mea of x

• 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

• measures size of prediction errors
• vertical distance btwn point and regression line
• Y- Y^       <---(y hat) 
• Large residual = unusual observation

Least Squares Method

Yields the regression line

• Σ(residuals)²
• Least squares regression line = line that minimizes vertical distance btwn points and their predictions
• Slope = r( S_y / S_x )
• Y-Intercept = (Average of Y) - b * (Average of X)

• 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

• Using regression line to predict y-values for x-values outside observed range of data

• Observation that lies far away from trend that rest of data follow

• 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.

• Unobserved variable that influences association btwn variables of primary interest
• Not measured in study

• 2 explanatory variables both associated w/ a response variable but also associated with each other

• When direction of association between 2 variables changes after including 3rd variable and analyzing data at separte leves of that variable