Chapter 2 Section 2

1
Chapter 2 Section 2

• Correlation

2
Correlation

• Straight-line (linear) relations
• A linear relation is strong if the points lie
  close to a straight line.
• A linear relation is weak if the points are
  widely scattered about the line
• Since eyes can be fooled, we use correlation
• The correlation measures the direction and
  strength of the linear relationship between two
  quantitative variables. Pg 127, formula.

3

• Correlation makes no use of the distinction
  between explanatory and response variables.
• Both variables must be quantitative.
• Does not change when we change the units of
  measure.
• Positive r is positive association
• Negative r is negative association
• 0 indicates weak linear relationship.
• -1 or 1 indicate strong linear relationships.
• Measures the strength of only the linear
  relationship between 2 variables
• Not resistant.

4

• Correlation is not a complete description of
  bivariate data.
• You should also mention the mean and standard
  deviation.
• Daily Work pp 131-135
• 20, 22, 24, 28

5
Chapter 2 Section 3

• Least-Squares Regression

6
Regression Line

• A regression line is a straight line that
  describes how a response variable y changes as an
  explanatory variable x changes.
• It predicts the value of y for a given x.
• Regression requires an explanatory variable and a
  response variable.

7
Fitting a line to data

• Fitting a line means drawing a line that comes as
  close as possible to the points.
• y a bx

8
Extrapolation

• Extrapolation is the use of a regression line for
  prediction far outside the range of values of the
  explanatory variable x that you used to obtain
  the line.

9
Least-squares Regression

• The least-squares regression line of y on x is
  the line that makes the sum of the squares of the
  verticle distances of the data points from the
  line as small as possible.
• y a bx
• With slope b r(sy/sx)
• And intercept a y bx

10
Interpreting the regression line

• A change of one standard deviation in x
  corresponds to a change of r standard deviations
  in y.
• The least-squares regression line always passes
  through the point (mean x, mean y)

11
Correlation and regression

• r squared in regression
• The square of the correlation, r squared, is the
  fraction of the variation in the values of y that
  is explained by the least-squares regression of y
  on x.
• Give an r squared as a measure of how successful
  the regression was in explaining the response.

12
Daily Work pp 148-153

• 36, 38, 40, 42, 48