Correlation -> Linear Regression

Question 1

CORRELATION

Answer 1

• measures “degree of association” between 2 scale (interval/ratio)/ordinal (ordered category) variables

Question 2

ASSOCIATIONS

Answer 2

• measured in “r” (parametric/Pearson’s)/”p” (non-parametric/Spearman’s)
• unless both variables = normally distributed, Spearman’s MUST be used
  POSITIVE
• increase in 1 variable = associated w/increase in other
  NEGATIVE
• increase in 1 variable = associated w/decrease in other

Question 3

CORRELATION (EXAMPLES)

Answer 3

• comparing 2 variables in degree of association terms (ie. attitude scales VS behavioural frequency)
• test statistic = r (parametric)/p (non-parametric) (aka. -1 = perfect negative correlation; 0 = random distribution zero correlation; +1 = perfect positive correlation)

Question 4

CORRELATION: HEIGHT VS WEIGHT

Answer 4

• strong positive correlation between height/weight
• can see how relationship works BUT cannot calculate one from other
• causal inference (?); aka. is 1 variable dependent on other? are both influenced independently by third variable?
• ie. if 120cm tall, how heavy (approx.)?

Question 5

CORRELATION: SUMMARY

Answer 5

• association tests use “correlation coefficient” to assess how strongly/in what direction 2 continuous variables are associated
• CANNOT tell us anything about causal inferences aka. cause-effect direction of relation; logic only sometimes determines this

Question 6

CORRELATION: ANOVA EXAMPLE

Answer 6

• eg. one-way ANOVA w/contrasts
• tells us (ie.) if treatment has effect on symptom index BUT not anything about relation between amount of A/B drug/symptoms experienced by patient
• correlation = strong & negative; shows relation but not predictions

Question 7

LINE OF BEST FIT

Answer 7

• allows to describe relationship between variables more accurately
• can now predict specific values of 1 variable from knowledge of other
• all points should be close to it

Question 8

RESIDUAL VALUE

Answer 8

• can predict specific values of 1 variable from knowledge of another via simple regression/best fit line
• BUT will predictions be as accurate? NO; via “residual value”
• aka. dif between observed value of DV (y-axis) VS predicted by equation

Question 9

GENERAL REGRESSION RULES

Answer 9

• DV should be measured on interval/ratio (continuous) scale variable
• ordinal usually good in practice so long as we have large enough category number (7+) & frequency distribution = normal
• IVs should be measured on interval/ratio scales
• BUT… most ordinal measurement = acceptable in practice (apply same rules as ordinal DVs)
• dichotomies/binary variables = also OK as IVs
• distributions of variables should be roughly normal; correlation/regression = sensitive to shape of frequency distribution of variables (unlike ANOVA)
• regression/associated techniques = robust BUT w/limits
• if not roughly normal can be corrected via appropriate transformation (ie. taking logarithms of all measurements)
• 2-valued categorical variables (dichotomies/binary variables) can be used directly as regressors (ie. yes/no)
• categorical variables w/3+ categories are dealt w/via dummy variables

Question 10

ANOVA VS MULTIPLE REGRESSION

Answer 10

DVs
- ANOVA/regression = continuous only
IVs
- ANOVA = category only
- regression = both continuous/category

Question 11

SUMMARY

Answer 11

1-WAY ANOVA
- continuous (DV) -> category (IV (1))
2-WAY ANOVA
- continuous (DV) -> category (IV (1)) + category (IV(2))
SIMPLE LINEAR REGRESSION
- continuous (DV) -> continuous (IV (1))
MULTIPLE LINEAR REGRESSION
- continuous (DV) -> continuous (IV (1)) + continuous (IV (2)) + …