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Flashcards in Linear Regression Deck (39):
1


Regression Analysis uses a _______model to predict a  ______variable (dv) by using one or more _______variables (iv).

Statistical

Response

Predictor

 

2


In regression analysis, β0 and β1 are called_______

parameters

3

What are the four steps of hypothesis testing?


Step 1:

one-sided: H0<μ  Ha≥μ(no linear association between x and y – not useful for predicting y)

two-sided: H0=μ  Ha≠μ

Step 2:

t=(x ̅-μ0)/(s⁄ √n) with df=n-1
t*=b1/s{b}

Step 3: t {1- α, n-1} OR t {1- α/2, n-1}

Step 4: If t ≥ +crit val or ≤ -crit val reject H0

4


What is the simple linear regression model?

Y=β01X1

5


In linear regression, E(ε)=

0

6


In linear regression, σ2 {ε}=

σ2

7

In linear regression, ε’s are/are not correlated and have covariance of ___.

ε’s are uncorrelated and have covariance of 0

8


Least Squares Estimates of betas _____ the sum

                                  n

                                  ∑   [y1-(β01xi)]2

                                (i=1)

minimize

9


Interpretation of β1

Y=β01X1

For each increase in x, there is an increase/decrease in y.

 

(e.g., For each add’l hour a student watches tv, he loses .2 GPA points)

10


Interpretation of β0

Y=β01X1

The mean when x=0

(e.g., On average, first year students who don’t watch tv have a GPA of 3.9)

11

y ̂ is the ____ regression line.

estimated

12


b1 and b0 are estimates for

β1 and β0

 

13


What is the equation for b1

(ssxy)/(ssxx

14


What is the equation for b0

y ̅   -   b1x ̅

15


What is the equation for SSxx

All of the following equations are equal

∑(xi - x ̅ )2

(∑x i2) - n(x ̅ )2

(n-1) sx2

16

SSxx must be positive/negative.

positive

17

What is the equation for SSxy

 

∑(xi - x ̅ ) (y - y ̅ )

(∑xiyi) - n(xy̅)

18

When creating a table for an estimated regression line, which 5 columns should you include?

xi     |    yi     |     xi2     |    yi2    |    xiyi

19

What is the equation for the residual εi

εi = yi-E(yi)

20

What is the equation for the residual ei

ei = yi - y ̂i

21

s2 is the ________

sample variance

22

What is the equation for s2

All of the equations below are equal

(∑(xi-x ̅ )2) / (n-1)

SSE/(n-2)

MSE

23


s is the ____________

sample standard deviation

24


What is the equation for s

√MSE

√(SSE/(n-2))

25

SSE is


The sum of the squared errors

26


What is the equation for SSE

All of the equations below are equal

∑ei2

∑(yi - y ̂i)2

ssyy - b12ssxx

27


What does s2=.045 and s= .212 mean?

If the dist of GPA for ppl who watch x hrs of tv is approx. normal, then about 95% of them are expected to have GPAs within 2(.212) units of their simple linear reg model

28

You should assume ____ for hypothesis testing and confidence intervals

normality

29

b1 and b0 are _______ for β1 and β0

least squares estimators

30


Why do you want to have a large range of data?

The more variation you have, the better estimate of the slope you can get..

31

 

sampling distribution of __(b1)_need to check this_?

has a t-distribution of n-2,

because we estimate b0 and b1

32


What does it mean to have a 95% CI?

If we took 100 samples of size xx, we would expect 95% of tem to contain value β1

Interpretation: 95% of all b1’s will fall within this range

33

What is Interval Estimation?

CI for mean of Y when x=xh

34


SSTo

the error/variation when not using any model at all; never changes when using a diff model or using new variables; total var around y ̅

35


SSE


error/variation when using SLR; the variation in y not explained by using x; too high equals too much error

36


SSR


The error left after fitting the model; the chunk of variation in y explained by using x (we want this to be large)

37

What are the components of the ANOVA table?

Source of Variation        SS            df               MS
Regression                   SSR     ÷    1         =   MSR
Error                                SSE     ÷   n-2       =   MSE
Total                                SSTo         n-1

 

38


What does an F-test for model usefulness tell us

if R2 is signif, but not if it is useful

39


What are the four steps in conducting an F-test

Step 1:

two-sided: H01=0      Ha: β1 ≠ 0

Step 2: F*=MSR/MSE  =SSR/MSE                                         (all are always positive; want F* to be >1)

Step 3: F {1-α, 1, n-2}      (*numerator df always 1 in SLR)

Step 4: if F* > F {1-α, 1, n-2}, we reject H0and we have evidence that the SLR model is useful

*in SLR (one predictor variable), the t-test for β1=0 is the same as the F-test
*In SLR only F* = t*2     √(fcrit) = tcrit