Question

5) Based on quarterly data collected over the last four years, the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: t= 3,305 – 665 Qtr1 – 1,335 Qtr 2 + 305 Qtr3, where Qtr1,Qtr2, and Qtr3 are dummy variables corresponding to Quarters 1, 2, and 3. The demand forecast for Quarter 2 of the next year is ________.

A) 2,640

B) 1,970

C) 3,610

D) 3,305

2) In a two-way ANOVA test, how many null hypotheses are tested?

A) 1

B) 1 or 2

C) 2 or 3

D) More than 3

3) The following is an incomplete ANOVA table.

source of variation	ss	df	ms	f
between groups		2	12.5
within groups
total	100	10

For the within groups category, the degrees of freedom are ________.

A) 6

B) 7

C) 8

D) 9

6) Costco sells paperback books in their retail stores and wants to examine the relationship between the prices and sales. The price of a particular novel was adjusted each week and the weekly sales are in the following table. Management would like to use a simple linear regression model that uses prices to predict sales.

sales	prices
7	12
4	11
5	10
9	9
8	8
8	7
7	7

The predicted weekly sales for the novel when priced at $10 is equal to ________.

A) 4.60

B) 5.07

C) 6.45

D) 7.33

2) Which of the following is the 95% confidence interval for the regression coefficient β1 if df=30, b1= −2 and s= 3?

A) [−5.00, −1.00]

B) [−7.88, 3.88]

C) [−7.09, 3.09]

D) [−8.13, 4.13]

Answer 1

5) t = 3305 - 665 Qtr1 - 1335 Qtr 2 + 305 Qtr3,

The demand forecast for Quarter 2 of the next year is

t = 3305 - 665*0 -1335*1 + 305*0 = 1970

Answer B)

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2) In a two-way ANOVA test, number of null hypotheses that are tested:

Answer: C) 2 or 3

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3)

For the within groups category, the degrees of freedom are 10-2 = 8

Answer: C) 8

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4)

X	Y	XY	X²	Y²
12	7	84	144	49
11	4	44	121	16
10	5	50	100	25
9	9	81	81	81
8	8	64	64	64
7	8	56	49	64
7	7	49	49	49
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
64	48	428	608	348

Sample size, n =	7
x̅ = Ʃx/n = 64/7 =	9.142857143
y̅ = Ʃy/n = 48/7 =	6.857142857
SSxx = Ʃx² - (Ʃx)²/n = 608 - (64)²/7 =	22.85714286
SSyy = Ʃy² - (Ʃy)²/n = 348 - (48)²/7 =	18.85714286
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 428 - (64)(48)/7 =	-10.8571429

Slope, b = SSxy/SSxx = -10.85714/22.85714 = -0.475

y-intercept, a = y̅ -b* x̅ = 6.85714 - (-0.475)*9.14286 = 11.2

Regression equation :

ŷ = 11.2 + (-0.475) x

Predicted value of y at x = 10

ŷ = 11.2 + (-0.475) * 10 = 6.45

Answer: C) 6.45

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5)

Critical value, t_c = T.INV.2T(0.05, 30) = 2.0423

95% Confidence interval for slope:

Lower limit = b1 - tc*se(b1) = -2 - 2.0423*3 = -8.13

Upper limit = b1 + tc*se(b1) = -2 + 2.0423*3 = 4.13

Answer: D) [−8.13, 4.13]