Question: QUESTION 1 Given the model y = + 1 X 1 + 2 X 2 + 3 X 3 + and n = 20, what

QUESTION 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

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

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

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

QUESTION 9

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

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

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

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

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

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

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

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

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

E() = 0

True

False

QUESTION 22

Var() = ² and is non constant

True

False

QUESTION 23

has a normal distribution

True

False

QUESTION 24

The error terms are dependent.

True

False

QUESTION 25

The range of R² is -1 2

True

False

QUESTION 26

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

True

False

QUESTION 27

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 + ₂I_F + ₃I_D
	B.	_o + ₁X₁ + ₃ +
	C.	_o + ₁X₁
	D.	_o + ₁X₁ + ₃

QUESTION 29

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

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

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

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

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

SSE = ____

QUESTION 40

S² = ____

QUESTION 41

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

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

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

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

R² = ____

QUESTION 48

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

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

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?

Do not reject Ho

Reject Ho

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?

is not

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

QUESTION 1 Given the model y = + 1X1 + 2X2 +

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