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MGT611AC-FA18-Exam1-ReviewProblems-Solutions-Typed.pptMGT611ONLAC:
Advanced Quantitative Methods
Christopher P. Wright
Exam 1 Review Problems
Review Problems
The production manager at Saulsbury Fire Rescue (my old company) is trying to create a model to determine the production time (in hrs) of its custom rescue trucks. Characteristics that are believed to play a role include the length (in ft) of the body (“length”), the weight (in lbs) of equipment to be carried (“equipment”) and the number of trucks in production (“trucks”) at the time. The values for 36 random rescues were recorded:
Create a linear model, run the regression and interpret the results. Use α = 0.05. Be sure to check for fit and relationships (overall and individual significance), as well as interpret the coefficients.
Review Problem - Regression
Review Problem – Regression
Dependent variable: Hours (what we’re explaining)
Independent variables: Length, Equipment
and Trucks
Model (population relationship):
Hours = β0 + βLLength + βEEquipment + βTTrucks + ε
(what we’re using
to explain it)
= -57.5 + 6.67 Length + 0.014 Equipment + 2.74 Trucks
Estimated regression equation (based on this sample):
Est.’d mean
hours
= -57.5 + 6.67(20)+ 0.014(5000) + 2.74(10)
Estimating mean for 20’ body, carrying 5,000 lbs with 10 tucks ahead of it:
Est.’d mean
hours
= 174.88 hours
Review Problem – Regression
b0 = -57.5 Trucks that are 0’ long, designed to carry 0 lbs
and with 0 trucks ahead, are estimated to take
-57.5 hours, on average.
bL = 6.67 For each additional foot of length, hours are
estimated to increase by 6.67, on average, holding all else (equip. and trucks) constant.
bE = 0.014 For each additional pound of equipment, hours are estimated to increase by 0.014, on average, holding all else (length and trucks) constant.
bT = 2.74 For each additional truck ahead, hours are
estimated to increase by 2.74, on average, holding all else (length and equip.) constant.
Estimating coefficients:
Lab Exercise 2
R 2 = 0.456 (45.6%)
Assessing fit: This not near 1 (perfect fit) or 0 (no fit). It is near 0.5, so the fit is good, but not great.
Literal interpretation: 45.6% of the variation in hours in the sample is explained by its (linear) relationships with length, equipment and trucks.
Overall significance (F-test)
p-value = 0.000188 < 0.05 (α)
- Reject H0 at a 5% significance level
There is sufficient evidence to prove that at least one population slope, βi , is not 0. Hours has a relationship with at least one of length, equipment and trucks. Yes, it is significant overall.
H0: βB = βS = βD = 0
HA: At least one population
slope, βi, is not 0
Lab Exercise 2
Individual significance (t-test)
H0: βi = 0
HA: βi is not 0
Length
p-value = 0.00288 < 0.05
- Reject H0 at a 5% significance level
There is sufficient evidence to prove that the population slope of
length, βL, is not 0.
Hours has a relationship with length.
Yes, length is individually significant.
Equipment
p-value = 0.01204 < 0.05
- Reject H0 at a 5% significance level
There is sufficient evidence to prove that the population slope of
equipment, βE, is not 0.
Hours has a relationship with equipment.
Yes, equipment is individually significant.
Lab Exercise 2
Individual significance (cont’d)
Trucks
p-value = 0.397 > 0.05
- FTR H0 at a 5% significance level
There is insufficient evidence to prove that the population slope of
trucks, βT , is not 0.
Cannot say if hours has a relationship with trucks.
No, trucks is not individually significant (based on this sample)
Review Problem - Regression
Is there any evidence of an interaction effect between length and equipment?
Rescue trucks come in two types: walk-in (contains crew area in middle of body) and non-walk-in (body only contains compartments.) How would you determine if there were a difference in the mean hours, holding all else constant, of the two types?
xint = length * equipment
p-value = 0.805 > 0.05 FTR H0 at a 5% significance level
There is insufficient evidence to prove that the population interaction coefficient, βint , is not 0.
Cannot say if length and equipment have an interaction effect
Make (arbitrarily) “walk-in” the base case.
Two cases means we need one dummy.
{
IsNW =
1 If truck is a non-walk-in
0 Otherwise
Review Problem - Regression
Length Equip.TrucksHoursLengthEquip.TrucksHoursLengthEquip.TrucksHours
216000122121563001012323570011256
15380010123234800121991551008148
23700092372180001319122500012234
23740072192254001319817710013229
196800112022258001021120660015241
226900131972271001216824490012205
214300151881449001114617470011153
23470010105238100826718530012208
183600121281649001220317520011160
21550081942253001217019580010175
23470012217165300111291945009208
17510010832366001222819430012142
