midterm Flashcards
TSS
variance * (n-1)
(yi-y-bar)^2
RSS
TSS-RegSS
(yi-y-hat)^2
RegSS
r^2=RegSS/TSS
so, RegSS= r^2 * 1/RSS
(Y-hat-y-bar)^2
r^2
Cov(x,y)/s(x)s(y)
OR
RegSS/TSS
OR
1-RSS/TSS
MS of the model
RegSS/df
MS of the residual
RSS/df
MS of the total
TSS/df
b
cov(x,y)/variance (x)
OR
r * (sy/sx)
t
b-B / SEb
RMSE
sqrt RSS/ n-1
SEb
sqrt(MSE/variance of x*n-1)
confidence interval
b plus or minus (t * SEb)
a
ybar-b*xbar
______: a fixed property of a population
Parameter
______: statistic we believe approximates the parameter
estimator
If the expected value does not meet the true parameter value, the estimator is _____
biased
What is the average difference between a single sample mean and the population parameter?
efficiency
More efficient estimators have ______ error variance
smaller
T/F: there is a tradeoff between efficiency and bias
true
MSE combines ____ and ______
bias and efficiency
Equation is variance + bias ^2
(bias is expected mean minus real world mean)
What is reliability?
Reliability is proportion of observed variance attributable to signal
What is the equation for reliability?
signal/(signal + noise)
What is the equation to calculate variance of a scale?
variance x1 + variance x2 + variance x3 +2(cov x1, x2+cov x1, x3 + cov x2, x3)
So you have the variance of a scale.. how do you partition which is noise and which is signal?
proportion signal = 1-(noise/total) or
1-(sum of variances/variance of whole scale (adding up variances and covariances))
What is the equation for alpha? in both symbol terms and context terms
(k/k-1)(1-(sum of variances of each item/variance of whole scale))
or number of items over number of items minus one times proportion signal
Cronbach’s alpha is an accurate measure of reliability for essentially tau-equivalent scales, which means it under-estimates reliability of items that are _____
congeneric, or have varying lambdas (scale not uniform)
Quantile distributions have a cumulative density function. What does this mean?
Let n = 100, so it ranges from 1 to 100•Sort on X from low to high.•The median observation is the value of X for observation i=50•zi=P-1(50/101)=P-1(.495)-0
More sensitive in the tails
Boxplots are very useful for comparing ______ distribution across levels of a _____ measure
quantitative, qualitative
relationships between quantitative measures can be explored using _____
scatterplots
What is the regression equation for observed values (not predicted values)?
y=a+bx+e
conditional mean + residual
What is a + bxi?
the conditional mean
What is the equation for a residual?
yi-a-bxi
OLS minimizes____
RSS
A change of one standard deviation in _ corresponds to a change of r standard deviations in _.
x, y
_ is symmetric, while _ is not
r, b
the slope on x on y is not necessarily the same as the slope of y on x
What is the equation for error variance? (MSE)
sum of E’s squared, or RSS,/n-k-1
What is the equation for standard error? (RMSE)
sqrt(sum of E’s squared, or RSS,/n-k-1)
What is the equation for r
Sxy/SxSy
