Chapter 4: Describing the Relation between Two Variables

Section 4.1: Scatter Diagrams and Correlation

Knowledge Prerequisites

1. declarative knowledge (definitions)
   1. Section 1.2:
      • explanatory variable
      • response variable
   2. Section 3.1:
      • resistant measure
2. procedural knowledge
   1. none
3. conditional knowledge
   1. Section 3.1:
      • explain why a measure is a resistant measure

Learning Goals

1. declarative knowledge (definitions)
   1. univariate data
   2. bivariate data
   3. scatter diagram (a.k.a., scatterplot)
   4. positive association
   5. negative association
   6. linear correlation coefficient, r (a.k.a., Pearson product moment correlation coefficient)
   7. properties of the linear correlation coefficient
   8. lurking variable
2. procedural knowledge
   1. How to calculate r with TI83/84: http://stats.jjw3.com/math1431/ti83corCoeff.htm
   2. How to construct a scatterplot with TI83/84 with TI83/84: http://stats.jjw3.com/math1431/ti83scatter.htm
3. conditional knowledge
   1. explain why r is not a resistant measure
   2. know the difference between correlation and causation
   3. identify possible lurking variables in bivariate data
   4. identify explanatory variables and response variables in bivariate data
   5. identify if bivariate data looks linear
   6. understand the linear correlation coefficient measures the degree of linear association and is not an appropriate measure of non-linear associations
   7. understand the linear correlation coefficient has no units and does not depend on the choice of unit for the explanatory and response variables
   8. identify if bivariate data has positive correlation, negative correlation, or no correlation
   9. match r-values with scatterplots
   10. describe relationships between variables graphed with scatterplots [linear, somewhat linear, not linear; positive association, negative association, no association; potential outliers]

Section 4.2: Least-squares Regression

Knowledge Prerequisites

1. declarative knowledge (definitions)
   1. Algebra:
      • how to plot points on coordinate axes
      • how to graph a line on coordinate axes
      • equation of a line
      • explain the meanings of slope and y-intercept of a line
   2. Section 4.1:
      • how to construct a scatterplot
2. procedural knowledge
   1. Section 4.1:
      • how to calculate r with TI83/84
3. procedural knowledge
   1. Section 4.1:
      • how to describe a scatterplot
      • identify if bivariate data looks linear
      • identify if bivariate data has positive correlation, negative correlation, or no correlation
      • match r-values with scatterplots
      • identify potential outliers in a scatterplot

Learning Goals

1. declarative knowledge (definitions)
   1. least-squares regression line,
2. procedural knowledge
   1. how to calculate the least-squares regression line with TI83/84: http://stats.jjw3.com/math1431/ti83lsq.htm
   2. how to make a prediction, y-hat, using least-squares regression line
3. conditional knowledge
   1. understand the linear regression is inapprorpiate for non-linear associations or when there is an outlier
   2. explain the meaning of slope and y-intercept of least-squares regression line
   3. understand the regression is used to estimate the average value of y when you know x
   4. determine when predictions based on least-squares regression line are not reasonable

Section 4.3: The Coefficient of Determination

Knowledge Prerequisites

1. declarative knowledge (definitions)
   1. Section 4.2:
      • least-squares regression line,
2. procedural knowledge
   1. Section 4.1:
      • how to calculate r with TI83/84
3. conditional knowledge
   1. Section 4.1:
      • how to describe a scatterplot

Learning Goals

1. declarative knowledge (definitions)
   1. coefficient of determination, r²
2. procedural knowledge
   1. How to calculate r² with TI83/84: http://stats.jjw3.com/math1431/ti83corCoeff.htm
3. conditional knowledge
   1. how to interpret r²
   2. match r²-values with scatterplots

Chapter 4: Required Formulas – Need to Know for Tests

1. Least-Squares Regression Line:
2. Coefficient of Determination [square the Linear Correlation Coefficient]: r²