Scatterplots & Correlation
What type of variables are displayed in a scatterplot?
Two quantitative variables
What is the equation of a regression line?
ŷ = a + bx
What is extrapolation?
Using the regression line to predict values outside the observed range.
Formula for relative frequency?
(# event occurrences) / (total trials).
Interpret P(A | B) in words.
“The probability of A given B.”
What does a positive correlation (r) indicate?
As one variable increases, the other also increases.
In the regression equation, what does b represent?
The slope, or the predicted change in y for each 1-unit change in x.
What is an influential point?
A data point that significantly affects the slope of the regression line.
Valid range of a probability?
From 0 to 1, inclusive.
In symbols, what does the vertical slash “|” mean?
“Given.”
What is the range of possible values for r?
From –1 to +1.
What does the y-intercept (a) represent?
The predicted y-value when x = 0.
Does correlation imply causation?
No, a strong correlation does not mean one variable causes the other.
When are two events independent?
When the outcome of one does not affect the other.
When are events disjoint (mutually exclusive)?
When they have no outcomes in common.
What does an r value close to 0 suggest?
A weak or no linear relationship.
What does the r² (coefficient of determination) tell us?
The percentage of variation in y explained by x.
What is a lurking variable?
An unmeasured variable that influences the relationship.
General addition rule: P(A or B) = ?
A: P(A) + P(B) − P(A and B).
If P(A) = 0.4 and P(B) = 0.5 and A, B are independent, find P(A and B).
0.20
What kind of relationship does correlation not measure well?
Nonlinear relationships or those influenced by outliers.
How does the least squares method determine the regression line?
It minimizes the sum of squared residuals.
Difference between lurking and confounding variables?
Lurking: not measured; Confounding: measured but entangled with other explanatory variables.
Multiplication rule for independent A and B?
P(A and B) = P(A) × P(B).
Define a probability model.
A specification of possible outcomes and assumptions/probabilities for events in the sample space.