QUESTION 1

1. Given the model y = + ₁X₁ + ₂X₂ + ₃X₃ + and n = 20, what are the degrees of freedom on the error?

	A.	16
	B.	19
	C.	17
	D.	20

QUESTION 2

Given y-hat = 25 + 7.5X₁ +26.5X₂ - 4.1X₁X₂, what is the predicted value of y

when X₁ = 15 and X₂ = 3?

	A.	25
	B.	32.5
	C.	224.5
	D.	409.3

QUESTION 3

1. Refer to problem 2. What is the residual when y = 29?

	A.	31.5
	B.	3.5
	C.	32.5
	D.	-3.5

QUESTION 4

1. Given y = + ₁X₁ + ₂X₂ + ₃X₃ + , if the plot of the residuals against the predicted values of y yielded a plot with a fanning out shaped pattern then which assumption is violated?

	A.	normality
	B.	mean 0
	C.	independence
	D.	constant variance

QUESTION 5

1. Given the model y = + ₁X₁ + ₂X₂ + ₃X₃ + if we plot y against X₁ and get a parabola shaped curve then what does this suggest?

	A.	E() does not equal zero
	B.	an X12 term is needed
	C.	an X22 term is needed
	D.	constant variance violated

QUESTION 6

Given the model y = + ₁X₁ + ₂X₂ + ₃X₁² + ₄X₂² + and with n = 20;

Which test do we use to test if the squared terms are significant to the model, when taken together?

	A.	Partial F-test
	B.	T-test
	C.	F-test
	D.	Durbin Watson

QUESTION 7

Given the model y = + ₁X₁ + ₂X₂ + ₃X₁² + ₄X₂² + and with n = 20;

Which test do we use to test if the model is useful?

	A.	T-test
	B.	F-test
	C.	Partial F-test
	D.	Durbin Watson

QUESTION 8

Given the model y = + ₁X₁ + ₂X₂ + ₃X₁² + ₄X₂² + and with n = 20

What is the null hypothesis for testing the squared terms as significant to the model when taken together?

	A.	Ho: 3 = 4 = 0
	B.	Ha: at least one beta not equal to zero
	C.	Ho: 3 = 0
	D.	Ho: 1 = 2 = 3 = 4 = 0

QUESTION 9

1. Refer to question 8. We can reject Ho if the partial F test statistic is _________. (with n= 20)

	A.	>3.06
	B.
	C.	>3.68
	D.

QUESTION 10

1. In the analysis of variance table (ANOVA) for any regression model, Sum of Squares error divided by degrees of freedom = ______________

	A.	mean square mode
	B.	R-squared
	C.	mean square error
	D.	F-value

QUESTION 11

1. In constructing a normal probability plot of the residuals, what shape is needed for normality to be satisfied?

	A.	linear
	B.	parabola shaped
	C.	bell shaped
	D.	S-shaped

QUESTION 12

1. In a multiple regression analysis, if the model provides a poor fit, then which of following will be true.

	A.	S2 will be small
	B.	SSE will be small
	C.	R2 will be close to 0
	D.	all of these

QUESTION 13

Which of the following variable selection techniques is a combination of the other 2 techniques that were discussed in the supplemental material folder?

	A.	Forward selection
	B.	Backward elimination
	C.	polynomial regression
	D.	Stepwise regression

QUESTION 14

Given the model y = + ₁X₁ + ₂X₂ + ₃X₁² + ₄X₂² + and with n = 25, which test do we use to test if X₂ is signficiant to the model?

	A.	F-test
	B.	Partial F-test
	C.	T-test
	D.	Polynomial test

QUESTION 15

1. Given the model y = + ₁X₁ + ₂X₂ + ₃X₃ + . We wish to check if the normality assumption is satisfed. Look at the normal probability plot that is in your handout, what can we conclude from this?

	A.	normality is satisfied
	B.	normality is seriously violated
	C.	constant variance is violated
	D.	constatn variance is satisfied

QUESTION 16

1. Given the model y = + ₁X₁ + ₂X₂ + ₃X₁² + ₄X₂² + and n = 25, what is the null hypothesis for testing if the model is useful?

	A.	Ho: 3 = 0
	B.	Ho: at least one beta not equal to zero
	C.	Ho: 3 = 4= 0
	D.	Ho: 1 = 2 = 3 = 4= 0

QUESTION 17

1. In problem 16 we reject Ho if F test statistic is > ________

	A.	2.87
	B.	3.10
	C.	2.84
	D.	2.76

QUESTION 18

1. Given the model y = + ₁X₁ + ₂X₂ + with n = 125, SSE = 585, Fcal = 10 and p-value = 0.006; What is your conclusion when testing if the model is useful?

	A.	The result is inconclusive
	B.	The model is not useful
	C.	The model is useful
	D.	the variables are dependent

QUESTION 19

Refer to problem 18. Now add 2 squared terms giving you a second order model.

y = + ₁X₁ + ₂X₂ + ₃X₁² + ₄X₂² + . Now with n =125, SSE = 334, What is your conclusion when testing if the squared terms are significant when taken together?

	A.	they are not significant
	B.	they are significant
	C.	the result is inclusive
	D.	none of these

QUESTION 20

1. Refer to Roman numeral I on your handout and answer question 20 below.

	A.	10 and 27
	B.	3 and 34
	C.	6 and 31
	D.	4 and 34

QUESTION 21

1. E() = 0

True

False

QUESTION 22

Var() = ² and is non constant

True

False

QUESTION 23

1. has a normal distribution

True

False

QUESTION 24

1. The error terms are dependent.

True

False

QUESTION 25

1. The range of R² is -1 2

True

False

QUESTION 26

1. The method of 'Least Squares is used to estimate the parameters in a regression model.

True

False

QUESTION 27

1. The log transformation of the y variable will never achieve constant variance when that assumption is violated.

True

False

QUESTION 28

Refer to roman numeral II on your handout.

According to the model, what is the E(Y) when the car is a dodge?

	A.	o + 1X1 + 2IF + 3ID
	B.	o + 1X1 + 3 +
	C.	o + 1X1
	D.	o + 1X1 + 3

QUESTION 29

1. Refer to question 28. According to the model, what is _D - _C?

	A.	3
	B.	o + 1X1 + 3
	C.	2- 3
	D.	2

QUESTION 30

1. Refer to question 28. According to the model, what is _F - _C

	A.	3
	B.	2
	C.	2 - 3
	D.	none of these

QUESTION 31

1. Refer to question 28. According to the model, what is _F - _D

	A.	2
	B.	3
	C.	2 - 3
	D.	none of these

QUESTION 32

For the rest of the exam refer to the JMP problem in roman numeral 3 of your handout.

Write down the first order linear model.

	A.	y = E(Y) +
	B.	y = o + 1x1 + 2x2 +
	C.	y = o + 1x1 + 2x2
	D.	none of these

QUESTION 33

1. Write down a second order linear model with interaction.

	A.	y = E(Y) +
	B.	y = + 1X1 + 2X2 + 3X12 + 4X22 +
	C.	y = + 1X1 + 2X2 +
	D.	y = + 1X1 + 2X2 + 3X12 + 4X22 + 5X1X2 +

QUESTION 34

Now using the JMP output for the second order linear model with interaction do problems 34 through 56.

34. Write down the prediction equation. y^ =

	A.	-68.27133+6.03652X 1 +0.44997X 2
	B.	-19.433779 - 3.73113X1 +0.67779X2 + 0.0576X12 - 0.0097X22 + 0.10643X1X2
	C.	-19.433779 - 3.73113 + 0.67779 + 0.0576 - 0.0097 + 0.10643
	D.	-91.2555 - 16.9756X 1 - 1.5128X 2- 0.4556X 1 2 - 0.0262X 2 2 + 0.4919X 1X 2

QUESTION 35

Refer to question 35 on your handout y^ =

QUESTION 36

1. Refer to question 36 on your handout: y - y^ =

QUESTION 37

Refer to question 37 on your handout and only fill in the blanks of the interval.

What is the 95% CI for E(Y)? (__________, ____________)

example answer is 5, 10 and note no rounding.

QUESTION 38

Refer to question 38 on your handout and only fill in the blanks of the interval.

What is the 95% PI for Y? (__________, ____________)

example answer is 5, 10 and note no rounding.

QUESTION 39

1. SSE = ____

QUESTION 40

1. S² = ____

QUESTION 41

1. S = ________

QUESTION 42

Refer to question42 on your handout and only fill in the blanks of the interval.

What is the 95% CI for ₂? (__________, ____________)

again no rounding and just numbers seperated by a comma

QUESTION 43

1. In testing if the diameter of a tree is significant, state the null and alternative hypothesis

	A.	Ho: 1 = 0 vs. Ha: 1 not= 0
	B.	Ho: 1 not= 0 vs. Ha: 1 = 0
	C.	Ho: 2 = 0 vs. Ha: 2 not= 0
	D.	none of these

QUESTION 44

1. Refer to question 44 on your handout. What is the test statistic?

QUESTION 45

Refer to question 45 on your handout. What is the correct decision?

QUESTION 46

1. Refer to question 46 on your handout. Which of the following is the correct conclusion?

	A.	There is enough evidence to say that the diameter of a tree is significant to the model
	B.	There is not enough evidence to say that the diameter of a tree is significant to the model
	C.	There is enough evidence to say that the model is useful.
	D.	There is not enough evidence to say that the model is useful.

QUESTION 47

1. R² = ____

QUESTION 48

1. Which of the following best interprets R²?

	A.	about R2% of the y values are predicted by X.
	B.	The model is accurate about R2% of the time.
	C.	about R2% of the variation in the y values is explained by this model
	D.	X1 and X2 predict y about R2% of the time

QUESTION 49

1. In testing if the model is useful, state the null hypothesis.

	A.	Ho:3=0
	B.	Ho:1 = 2 = 3= 4 = 5 =0
	C.	Ho: 3= 4 = 5 =0
	D.	none of these

QUESTION 50

Refer to question 50 on your handout: What is the test statistic?

QUESTION 51

1. Refer to question 51 on your handout, what is the correct decision?

	A.	Accept Ho
	B.	Do not reject Ho
	C.	Rejecth Ha
	D.	Reject Ho

QUESTION 52

Refer to question 52 on your handout. Is the following statement ture or false?

There is enough evidecne to say the model is useful.

True

False

QUESTION 53

Refer to question 53 on your handout; State the null hypothesis.

	A.	Ho: 3= 4 =0
	B.	Ho: at least one beta not equal to zero
	C.	Ho: 3= 4 = 5 =0
	D.	none of these

QUESTION 54

Refer to question 54 on the handout.

What is the correct decision?

	A.	Do not reject Ho
	B.	Reject Ho
	C.	Reject Ha

QUESTION 55

Refer to question 55 on the handout; In conclusion there ________ enough evidence to say the squared terms and the interaction term are significant to the model when taken together?

	A.	is
	B.	is not
	C.	none of these

QUESTION 56

For any given regression model and prediction equation if y = 99 and y-hat = 100 then E(Y) = ?

probability plot for number 15

\f\fIF = 1 if the car is a ford l if the car is a Dodge 10 otherwise and I, = 0 otherwise The director of operations has proposed the following model; y = Bo + BIX, + B2IF + BIDTE\f