STA 261 Chapter Notes - Chapter 3: Dependent And Independent Variables, Contingency Table, Frequency Distribution
21 May 2018
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Module Three: Association - Contingency, Correlation, and Regression
● Response variable: measured to make comparisons between groups
○ Result or response to variables
● Explanatory (predictor) variable: explains the value of the response variable
○ Variable that is manipulated
● Association: a relationship between two variables
○ Positive, negative, or no association
● Contingency table: a frequency distribution for bivariate data
○ Cell: each row and column combination
○ Joint event: event that has two or more characteristics
● Conditional proportions: proportions based on the explanatory variable for categories of
the response variable
● Correlation: a measure of the strength of the linear association between two variables
○ Linear or nonlinear
● Linear correlation coefficient, r
○ r = 1 means perfect positive linear correlation
○ r = -1 means perfect negative linear correlation
○ r = 0 means no linear correlation
○ Weak association
■ 0 < r < 0.4
■ -0.4 < r < 0
○ Moderate association
■ 0.4 < r < 0.8
■ -0.8 < r < -0.4
○ Strong association
■ 0.8 < r < 1
■ -1 < r < -0.8
● Regression equation (prediction equation)
○ Y-hat = a + bx
■ A = y-intercept
■ B = slope
○ X is the explanatory variable
○ Y-hat is the predicted mean value of the response variable
● Residuals
○ The differences between the observed and predicted values of the response
variable
○ E = y - y-hat
○ Each observation has a residual
■ If the observed value is larger than the predicted value then the point will
be above the line and the residual is positive
■ If the observed value is smaller than the predicted value, then the point is
below the line and the residual will be negative
● Coefficient of determination
