Formulas Exam 3 Flashcards
r
sample correlation
m
the number of predictor variables in regression
X i
a predictable variable in a regression. The subscript i represents any number from 1 through m
Y
the outcome variable that is being predicted or explained in a regression
Y- hat
the estimated outcome value as predicted by the regression equation
b i
the regression coefficient for predictor X i (sometimes written as b subscript* predictor name)
b 0
the intercept in the regression equation
sigma-b i
the standard error of a regression coefficient
SSy
the total sum of squares for the outcome of regression
SS regression
the sum of squares for the outcome in a regression
R squared
the proportion of variability explained by a regression
SS total
the total variability in the data for ANOVA
SS treatment
variability explainable by differences among groups (simple ANOVA) or measurements (repeated measures)
SS factor
variability explainable by main effect of some factor
SS A:B
variability explainable by interaction between factors A and B
SS residual
the residual sums of squares, representing the variability that can’t be explained in regression or ANOVA
MS effect
mean square for any effect we might want to test; the subscript can be regression, treatment, Factor, A:B etc
df effect
degrees of freedom for SS effect and MS effect, where effect is any effect we might want to test
MS residual
the residual mean square; used as an estimate of the population variance, sigma squared or sigma
df residual
the degrees of freedom for SS residual and MS residual
K
the number of levels of a factor (treatment) in ANOVA; written as k subscript* factor when there are multiple factors
M i
The sample mean of Group i in a simple ANOVA or measurement i in a repeated- measures ANOVA (i = 1 to k)
M s
the mean of all measurements from Subject s in a repeated-measures ANOVA to (s= 1 to n)
n i
the number of data (e.g. subjects) in Group i
M with line over it
the grand mean, i.e. the mean of all data in all groups taken together
