Chapter 3: Examining Relationships


Key Vocabulary:


§         response variable

§         explanatory variable

§         independent variable

§         dependent variable

§         scatterplot

§         positive association

§         negative association

§         linear

§         correlation

§         r-value

§         regression line

§         mathematical model

§         least-squares regression line

§           ”y-hat”

§         SSM

§         SSE

§         r2

§         coefficient of determination

§         residuals

§         residual plot

§         influential observation


 Calculator Skills:

§         seq(X,X,min,max,scl)

§         2-Var Stats

§         sum

§         Diagnostic On


§         Clear All Lists

§         residual plot

3.1    Scatterplots (pp.123-139)

1.      What is the difference between a response variable and an explanatory variable?

2.      How are response and explanatory variables related to dependent and independent variables?

3.      When is it appropriate to use a scatterplot to display data?

4.      Which variable always appears on the horizontal axis of a scatterplot?

5.      Explain the difference between a positive association and a negative association.

3.2    Correlation (pp.140-149)

1.      What does correlation measure?

2.      Explain why two variables must both be quantitative in order to find the correlation between them.

3.      What is true about the relationship between two variables if the r-value is:

  1. Near 0? 
  2. Near 1? 
  3. Near -1?
  4. Exactly 1?
  5. Exactly -1?

4.      Is correlation resistant to extreme observations?  Explain.

5.      What does it mean if two variables have high correlation?

6.      What does it mean if two variables have  weak correlation?

7.      What does it mean if two variables have  no correlation?

3.3    Least-Squares Regression (pp.149-180)

1.      In what way is a regression line a mathematical model?

2.      What is a least-squares regression line?

3.      What is the formula for the equation of the least-squares regression line?


4.      How is correlation related to least-squares regression?

5.      What is the formula for calculating the coefficient of determination?

6.      The  r2 value shows how much of the variation in one variable can be accounted for by the linear relationship with the other variable.  If r2 = 0.95, what can be concluded about the relationship between x and y?


7.      Define residual.

8.      If a least-squares regression line fits the data well, what characteristics should the residual plot exhibit?

9.      What is meant by an influential observation?