Homework 11 Written Doc
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School
Kansas State University *
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Course
351
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
docx
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2
Uploaded by DoctorKoupreyMaster4297
Homework 11
1.
Logistic Regression
a.
Fit a logistic regression predicting the probability that a person purchased Under
Armour gear in the last 3 years from their Age, their Age Squared, and the
StephFave dummy variable. Give the logistic regression equation. What R code
did you use to run your model?
P(Purchase) = [e^( -2.3916584+ 0.3298781(Age) -0.0057980(AgeSquared) +
1.6872251(FaveSteph))]/[1 + e^( -2.3916584+ 0.3298781(Age)
-0.0057980(AgeSquared) + 1.6872251(FaveSteph))]
AgeSquared = (UnderArmour$Age)^2
UnderArmour$AgeSquared = AgeSquared
lr = glm(Purchase ~ Age + AgeSquared + FaveSteph, data = UnderArmour, family =
binomial(link = "logit"))
summary(lr)
b.
Using the logistic regression, predict the probability that a 45 year old whose
favorite basketball player is Stephen Curry made an Under Armour purchase.
Also, predict the probability that a 65 year old whose favorite basketball player is
Joel Embiid made an Under Armour purchase.
i.
0.916761 or 91.6761%
j.
0.004294434 or 0.4294434%
numerator = exp(-2.3916584 + 0.3298781*(45) - 0.0057980*(45^2) +
1.6872251*(1))
denominator = 1 + numerator
numerator/denominator
numerator = exp(-2.3916584 + 0.3298781*(65) - 0.0057980*(65^2) +
1.6872251*(0))
denominator = 1 + numerator
numerator/denominator
c.
Compute the prediction accuracy of your logistic regression model. Give the R
code used to compute your prediction accuracy.
82.8%
> preds = ifelse(lr$fitted.values > 0.5, 1, 0)
> mean(preds == UnderArmour$Purchase)
d.
At the α = 0.05 significant level, for the logistic regression model, are people
whose favorite basketball player is Stephen Curry significantly more likely to
purchase Under Armour gear? Explain.
Yes, people whose favorite basketball player that is Stephen Curry are more likely
to purchase Under Armour gear because the p-value is less than the significant
level. (p-value = 2.140654e-11)
1-pnorm(6.594)
2.
Linear Probability Model
a.
Fit a linear probability model predicting the probability that a person purchased
Under Armour gear in the last 3 years from their Age, their Age Squared, and the
StephFave dummy variable. Give the equation of the linear probability model.
What R code did you use to run your model?
P(Purchase) = -9.639e-03 + 6.213e-02(Age) - 1.054e-03(AgeSquared) + 1.894e-
01(FaveSteph)
lpm = lm(Purchase ~ Age + AgeSquared + FaveSteph, data = UnderArmour)
summary(lpm)
b.
Using the linear probability model, predict the probability that a 45 year old
whose favorite basketball player is Stephen Curry made an Under Armour
purchase. Also, predict the probability that a 65 year old whose favorite
basketball player is Joel Embiid made an Under Armour purchase.
0.8407124 or 84.07124%
-0.4252961 or 0%
c.
Compute the prediction accuracy of your linear probability model. Give the R
code used to compute your prediction accuracy.
82.5%
preds2 = ifelse(lpm$fitted.values > 0.5, 1, 0)
mean(preds2 == UnderArmour$Purchase)
3.
From your analysis, which model would you prefer when predicting the purchase of
Under Armour gear? Why?
I would prefer to use the Logistic Regression model when predicting the purchase of
Under Armour because it will always give me a probability between 0-1, so there isn’t a
negative percentage or an over 100% percentage.
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