1
Q
Linear Regression
A
- Examine if two variables X and Y are linearly related or correlated.
- X is the independent or predictor variable.
- Y is the dependent variable or criterion variable.
2
Q
Explain this formula
Ŷ = a + bx
A
- Formula for a regression line; line of best fit
- Ŷ is the predicted value of Y (female systolic blood pressure).
- a is the Y-intercept (value of Y when x=0).
- b is the slope of the line (rate of change in Y for one unit of x) or regression coefficient.
- Example: Ŷ = 64.72 + 1.39 (age) for female systolic blood pressure)
3
Q
Distances between the regression line and data point are called ____.
A
- residuals
- Residuals are the degree of error in the regression line.
4
Q
How do we know how accurate our prediction is?
A
- coefficent of determination (r^2)
- Correlation of r=0.70 produces an r^2=0.49
– This indicates that 49% of the variance in Y is accounted for by knowing X. - R is important to know to understand variance
5
Q
Non-linear Regressions
A
- Quadratic and Cubic
- Quadratic is second term polynomial (two terms)
- Cubic is third order polynomial (three terms)
6
Q
Multiple Regression Models and Types
A
- More than one predictor variable being evaluated
- Minimum of 10 paricipants per predictor variable
Types:
* ENTER method
* Stepwise technique
* Hierarchial Regression
7
Q
ENTER method
A
- All predictors influence the equation whether they are a meaningful contribution or not
8
Q
Stepwise Technique
A
- Often used
- Statistical criteria maximizes prediction accuracy with the fewwst variables
- SPSS determines included and excluded variables
9
Q
Hierarchial Regression
A
- Researcher selects variables based on theory; Give researcher control of the model
- Researcher decides what is important and what has contributed to the prediction; look at r^2 after each variable and see how it affects the regression.
10
Q
Logistic Regression
A
- Uses dichotomous variables (live/dead, pahtology/no pathology; 0/1)
- Often used in epidemiological research
- Similar to multiple regression
– Coefficents for each predictor variable
– - Represents how the odds of getting the disease will change with a one-unit change in the exposure variable (IV).
11
Q
What is analysis of covariance?
A
- Statistical way to control for confounding factors in the analysis stage
- Often used to scale individuals; Ex: BW and Force Generated
12
Q
ANCOVA
A
- Combination of analysis of variance and linear regression
- Used to compare groups on a dependent variable groups differ on some relevant characteristic, called a covariate, before treatment
- Equates the two groups, based on covariate. Develop a regression line for each group based on covariate. Means are adjusted so comparisons can be made.
- Ex: Teaching strategies on performance in students; Use GPA as a covariate if suspected confounding variable (Unequal groups).
13
Q
Covariate must have a ____ relationship based on the measures.
A
linear
14
Q
What does it mean when a covariate is significant?
A
- Means it has an influence on the between group comparision
- This influence may be positive or negative
- Does not mean a signficant difference lies for between groups
15
Q
Asssumptions for ANCOVA
A
- Linearity of covariate (High r is important!)
- Independence of covariate (Can’t use look at velocity and distance as two seperate measures because they overlap)
- Good reliability of covariate (Ex: BW)
These are same as ANOVA
16
Q
What happens when you have too many covariates?
A
- Decreases the degrees of freeedom and loses power
- Therefore less likely to find a difference.
17
Q
Why do we use ANCOVA?
A
- Can increase sensitivity of a test by removing bias
- Used when researches cannot have control of all relevant variables.
18
Q
Limitations of ANCOVA
A
- Adjust means are NOT real scores, generalizability may be compromised
- Quantitaive variables work better than qualitative ones.
- If covariate is not reliable, will introduce its own bias.
