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Material Type: Exam; Class: Regression Analysis; Subject: Business Administration; University: University of Southern Mississippi; Term: Fall 2005;

Typology: Exams

Pre 2010

1 / 11

Download Exam 2 Solution Key - Regression Analysis | BA 303 and more Exams Introduction to Business Management in PDF only on Docsity! Name:
Student ID:
You have 70 minutes to complete this exam. You may use calculators subject to the caveats identified in the course
syllabus. You may not consult any other resources which have not heen provided in the exam package.
Multiple Choice
ldentify the letter of the chotce that hest completes the statement or answers the question.
Kach question is worth 2 paints,
_B |. The standard error is the
a. (statistic squared
b. square root of SSE
c. square root of SST
d, square root of MSE
I
If MSE is known. you can compute the
a. r square
b. coefficient of determination
c. standard error
d. all of these alternatives are correet
A 3. In regression analysis, which of the following is not a required assumption about the error tern €?
a. The expected value of the error term is one.
b. The variance of the error term is the same for all values of X
ce. The values of the error term are independent,
d. The error term is normally distributed.
A 4. In regression analysis, the variable that is being predicted is the
a. dependent variable
b. independent variable
¢. intervening variable
d. is usually x
Ihe equation that describes how the dependent variable (y) is related to the independent variable (x) is called
a. the correlation model
b, the regression model
e. correlation analysis
d. None of these alternatives is correct.
In a regression and correlation analysis if r’ = 1, then
SSL = SST
Ss l
SSE
ssT
aes
SSR
Name:
lwo
9.
HH.
SSE can never be
a, larger than SST
b. smaller than SSI
ce. equal to |
d. equal to zera
A repression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following
equation
Y=9-3X
The above equation implies that if the price is increased by $1, the demand is expected to
a. inercase by 6 units
b. deerease by 3 units
c. decrease by 6,000 units
d. decrease by 3.000 units
If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by
the variation in the independent variable
a. is 090%
b. is 90%,
cis 0.81%
d. can be any positive valuc
Exhibit 14-8
The following information regarding a dependent variable Y and an independent variable X is provided
YX = 90 EY-Y)OCX) — «156
Ey=340 D(X-X)-234
n-10 Ecy-Yy? — 1974
Refer to Exhibit 14-8, The total sum of squares (SST) is
a -156
» Re SST= Ty) >
Refer to Exhibit 14-8. What is the mean square error (MSE) (This one is a little tricky. 1int: you will need to
compute the correlation coefficient and use this to compute the coeffieient of determination)
a, 1870
)
b. 13
e 1974
d. 233.78
w
name:
Problem
21
{/2 points? Identify the null and alternative hypotheses for the following problems.
a ‘The manager of a restaurant believes that it takes a customer more than 25 minutes to cat Junch
a a1. weston
He ome te biswlld dex accept Oerded
i: aS RS tome ag. Od
Yia<as
b, Economists have stated that the marginal propensity to consume is at least 90¢ oul of every dollar.
I, A 2 me Peo
Ket M<AB Yoo
c. It has heen stated that 75 out of every 100 people who go to the movies on Saturday night buy
popcorn,
: . 7
Ms me
Ye. an x 25
a xz
Name:
22, {12 points} Ahmadi, Inc, has been manufacturing small automobiles that have averaged 50 miles per gallon
of gasoline in highway driving, The company has developed a more efficient engine for its small cars and
now advertises that its new small cars average more than 50 miles per gallon in highway driving. An
independent testing service road-tested 64 of the automobiles, The sample showed an average of 51.5 miles
per gallon with a sample standard deviation of 4 miles per gallon.
a Formulate the hypotheses to determine whether or not the manufacturer's advertising campaign is
legitimate.
Yi As 5o
Ui A >So
b. Compute the test statistic.
= es
=z % - Ke a Fer ie 3
A z —
nw 4
Fotis) £23}
A= 6# ML = So
©. What is the critical t-valuc (ic, that -value which determines the rejection bound) and what is your
conelusion? Use a = .05.
With A-1= G34 the critical A-valre i's:
As 107
Shae A+
lig. = 1.67) | reject No, Fah de
That tthe advertising Comp aigh
's Leg ighimat
Name:
23. {43 points{ Shown below is a partion of an Exec] outpul for regression analysis relating Y (dependent
variable) and X (independent variable),
ANOVA | ae
of SN See Full FOE | en
Regression 1 110 $5R F, t
Residual 8 ™ Sse Tink oof
Total 9 184 esr
Coefficients Standard krror
Intercept 39.222 be 5.943 Si.
x . 20.5556 py 0.1611 Sy,
a What has been the sample size for the above?
‘pl Keg. rn de!
rerall, tt observetlons fo the Simple i - ?
is found trom!
= —_ =h-
Af tole/ = rl »
Pn=/0
b. Perform attest and determine whether or not X and ¥ are related. Let @ — 0.05 and note that there
are & degrees of freedom. , = :
: " Hs Bree, nF? 2,306
je Ba, TE, 8. be
= = —
S ©, let} = oF
b,
- re ect He fence Ras 8 Sign) fi Conk
t wt luware om ¥
c. Perform an F test and determine whether or not X and Y are related. Let a = 0.05 and note that there
arc | numerator and 8 denominator degrees of freedom,
= sR = oO sige Mak = 5,32
ae Ase as
Shee PZ Fooc reject
Ye.
a a
en . 2H, ae Mote. Fatl.g7= C34) =4
h-a 3 a
y
eR > SK = No
1
MSE
Name:
(ivy
13
Wy)
eit
SST SSR+ SSE
SRF he
(vi)
2.75
(ppg FF
MERZ ssh = 22s
1 i
(vii}
O49
r 7 b, 6.a5 =O. ¥70/
e 0.5)0|
ANS:
a through d
Summary Output
Regression Statistics
Multiple R 0.7732
R Square 0.5978
Adjusted R. Square 0.5476
Standard Error 3.0414
Observations 10
ANOVA
df SS MS BF Significunce F
Regression 1 110 110 11.892 9.009
Residual 8 74 9.25
Total 9 184
Coefficients — Stendard Error ( Stat P-value
Intercept 39.222 5.942 6.600 0.000
x -0.556 O.161 -3.448 0.009
¢, 59.783% of the variability in Y is explained by the variability in X,
ANS:
Summary Output
REST ESSHOR SQUIRES
Multiple R 0.1347
K Square 0.0181
Adjusted R Square -0.0574
Standard Error 3.384
Observations 5
ANOVA
df SS MS FF Significance ¥
Repression 1 2.750 2.75 0.2402 0.6322
Residual 13 148.850 11.45
Votal 14 151.600
Coefficients Standard Frror__t Stat P-value
Intercept 8.6 2.2197 3.8744 0.0019
x 0.25 0.5101 0.4901 0.6322
we
ID: A

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