midterm

Question 1

TSS

Answer 1

variance * (n-1)

(yi-y-bar)^2

Question 2

RSS

Answer 2

TSS-RegSS

(yi-y-hat)^2

Question 3

RegSS

Answer 3

r^2=RegSS/TSS
so, RegSS= r^2 * 1/RSS

(Y-hat-y-bar)^2

Question 4

r^2

Answer 4

Cov(x,y)/s(x)s(y)

OR

RegSS/TSS

OR

1-RSS/TSS

Question 5

MS of the model

Answer 5

RegSS/df

Question 6

MS of the residual

Answer 6

RSS/df

Question 7

MS of the total

Answer 7

TSS/df

Question 8

b

Answer 8

cov(x,y)/variance (x)

OR

r * (sy/sx)

Question 9

t

Answer 9

b-B / SEb

Question 10

RMSE

Answer 10

sqrt RSS/ n-1

Question 11

SEb

Answer 11

sqrt(MSE/variance of x*n-1)

Question 12

confidence interval

Answer 12

b plus or minus (t * SEb)

Question 13

a

Answer 13

ybar-b*xbar

Question 14

______: a fixed property of a population

Answer 14

Parameter

Question 15

______: statistic we believe approximates the parameter

Answer 15

estimator

Question 16

If the expected value does not meet the true parameter value, the estimator is _____

Answer 16

biased

Question 17

What is the average difference between a single sample mean and the population parameter?

Answer 17

efficiency

Question 18

More efficient estimators have ______ error variance

Answer 18

smaller

Question 19

T/F: there is a tradeoff between efficiency and bias

Answer 19

true

Question 20

MSE combines ____ and ______

Answer 20

bias and efficiency
Equation is variance + bias ^2
(bias is expected mean minus real world mean)

Question 21

What is reliability?

Answer 21

Reliability is proportion of observed variance attributable to signal

Question 22

What is the equation for reliability?

Answer 22

signal/(signal + noise)

Question 23

What is the equation to calculate variance of a scale?

Answer 23

variance x1 + variance x2 + variance x3 +2(cov x1, x2+cov x1, x3 + cov x2, x3)

Question 24

So you have the variance of a scale.. how do you partition which is noise and which is signal?

Answer 24

proportion signal = 1-(noise/total) or

1-(sum of variances/variance of whole scale (adding up variances and covariances))

Question 25

What is the equation for alpha? in both symbol terms and context terms

Answer 25

(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

Question 26

Cronbach’s alpha is an accurate measure of reliability for essentially tau-equivalent scales, which means it under-estimates reliability of items that are _____

Answer 26

congeneric, or have varying lambdas (scale not uniform)

Question 27

Quantile distributions have a cumulative density function. What does this mean?

Answer 27

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

Question 28

Boxplots are very useful for comparing ______ distribution across levels of a _____ measure

Answer 28

quantitative, qualitative

Question 29

relationships between quantitative measures can be explored using _____

Answer 29

scatterplots

Question 30

What is the regression equation for observed values (not predicted values)?

Answer 30

y=a+bx+e

conditional mean + residual

Question 31

What is a + bxi?

Answer 31

the conditional mean

Question 32

What is the equation for a residual?

Answer 32

yi-a-bxi

Question 33

OLS minimizes____

Answer 33

RSS

Question 34

A change of one standard deviation in _ corresponds to a change of r standard deviations in _.

Answer 34

x, y

Question 35

_ is symmetric, while _ is not

Answer 35

r, b

the slope on x on y is not necessarily the same as the slope of y on x

Question 36

What is the equation for error variance? (MSE)

Answer 36

sum of E’s squared, or RSS,/n-k-1

Question 37

What is the equation for standard error? (RMSE)

Answer 37

sqrt(sum of E’s squared, or RSS,/n-k-1)

Question 38

What is the equation for r

Answer 38

Sxy/SxSy