Lesson 3- Bivariate Data Analysis

Question 0

Correlation Coefficient r

Answer 0

Scatterplot and r

• positive
• negative
• strong ( |r| -> 1 )
• weak (snowflakes, |r| -> 0 )
• r X slope

Question 1

Scatterplots

Answer 1

• 2 datas
• strength of a relationship
• predicting further results using functional expression

Question 2

Correlation Coefficient Properties

Answer 2

• positive (negative) r implies positive (negative) association
• correlation coefficient r has values between -1 and 1
• weak relationship r -> 0, strong relationship r -> 1, -1
• association X implies causation (causality: one causes another: fire and firemen)

Question 3

Correlation Coefficient properties 2

Answer 3

• r value has meaning only when linear relationships is assumed
• x and y must be quantitative (X categorical)

-x (explanatory variable) and y (response variable) are
indistinguishable; if x and y are switched, r value won’t change

• changing units in x or y has X effect on r: cause it’s fraction
• r is not resistant to outliers

Question 4

R^2

Answer 4

R^2 gives percentage of variation in y that is explained by the variation in x

Question 5

Least Squares Regression Line

Answer 5

LSRL

• y hat = a + bx
• best fitting straight line found by minimizing the sum of squares of residuals
• residual : y - y hat
• slope b=r(Sy/Sx), a from LSR passing through (mean x, mean y)

Question 6

Regression line

Answer 6

• distinguish b/w x and y ; regressions minimize residuals in y direction, not x
• if you graph z-scores of y against z-scores of x, slope of regression line = r, intercept = 0

Question 7

Regression chart

Answer 7

b = (seats), coefficient

a = constant, coefficient

r = square root ( R-sq )