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

§
r^{2}

§ 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:

- Near 0?
- Near 1?
- Near -1?
- Exactly 1?
- 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 *r ^{2} *value shows how much of the variation in one
variable can be accounted for by the linear relationship with the other
variable. If

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*?