Module 1.2 Goodness of Fit and Hypothesis Tests

Question 1

Total sum of squares (SST)

Answer 1

(actual Y values - mean Y value)^2

Question 2

Regression sum of squares (RSS)

Answer 2

(predicted Y values - mean Y value)^2

Question 3

Sum of squared errors (SSE)

Answer 3

(actual Y values - predicted Y values)^2

Question 4

Total variation =

Answer 4

explained variation + unexplained variation

Question 5

SST =

Answer 5

RSS + SSE

Question 6

RSS

Answer 6

explained variation

Question 7

SSE

Answer 7

unexplained variation

Question 8

degrees of freedom of explained variation

Answer 8

1

Question 9

degrees of freedom unexplained variation

Answer 9

n - 2

Question 10

total degrees of freedom

Answer 10

n - 1

Question 11

mean square regression (MSR)

Answer 11

= RSS

Question 12

Mean squared error (MSE)

Answer 12

= SSE/(n - 2)

Question 13

k =

Answer 13

number of slope parameters (degrees of freedom explained variable)

Question 14

standard error of estimate (SEE)st

Answer 14

square root of MSE

Question 15

percentage of total variation of the dependent variable explained by the independent variable

Answer 15

R^2

Question 16

R^2 =

Answer 16

regression sum of squares (RSS)/total sum of squares (SST)

Question 17

for simple linear regression, what is an alternative way to determine R^2?

Answer 17

r^2 (squaring correlation coefficient)

Question 18

assesses how well set of independent variables explains the variation in the dependent variable

Answer 18

F test

Question 19

used to test whether AT LEAST one independent variable in a set of independent variables explains a significant portion of the variation of the dependent variable

Answer 19

F statistic

Question 20

F statistic =

Answer 20

MSR/MSE

Question 21

how many tails is an F test?

Answer 21

one tailed

Question 22

what is the null hypothesis for an F test

Answer 22

b1 = X

Question 23

what is the alternate hypothesis for an F test?

Answer 23

b1 does not = X

Question 24

degrees of freedom for numerator (top part of fraction) for F test?

Answer 24

1

Question 25

degrees of freedom for denominator of F test?

Answer 25

n - k - 1 = n - 2

Question 26

decision rule for F test?

Answer 26

reject null if F statistic > critical value

Question 27

t statistic (n - 2 degrees of freedom) =

Answer 27

(point estimate - hypothesized value)/standard error of point estimate

Question 28

rejection of null in a t test means what?

Answer 28

slope coefficient is DIFFERENT from the hypothesized value

Question 29

t statistic for simple linear regression =

Answer 29

R * square root of (n - 2)/square root of (1 - r^2)

Question 30

smallest level of significance for which the null hypothesis can be rejected

Answer 30

p value

Question 31

tells us how the dependent variable moves in relation to independent variable

Answer 31

slope coefficient