Question
In: Statistics and Probability
Suppose that we have a single input variable X and all possible values of X is...
Suppose that we have a single input variable X and all possible values of X is {0, 1, 2}. Also, suppose that we have two groups for outcomes (i.e., Y = 1, 2). It is known that the X|Y = 1 has Binomial(2, 0.7) and X|Y = 2 has the discrete uniform. In addition, P(Y = 1) = 0.3.
(1) Predict Y for X = 0, 1, 2, respectively, using the Bayes classifier.
(2) Compute the overall Bayes error rate.
Solutions
orchestra answered 2 years agoRelated Solutions
Suppose the possible values of X are {xi}, the possible values of Y are {yj}, and...
Suppose the possible values of X are {xi}, the possible values
of Y are {yj}, and the possible values of X + Y are {zk}. Let Ak
denote the set of all pairs of indices (i,j) such that xi+yj
=zk;thatisAk ={(i,j):xi+yj =zk}
a. Argue that
b. Argue that
P{X+Y=zk}= ? P{X=xi,Y=yj} (i,j )∈Ak
E[X+Y]=? ? (xi+yj)P{X=xi,Y =yj} k (i,j )∈Ak
c. Using the formula in b, argue that E[X+Y]=??(xi+yj)P{X=xi,Y
=yj}
ij
d. Show that
P(X =xi)=?P(X =xi,Y =yj),P(Y =yj)=?P(X =xi,Y...
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X
Y
2
70
0
70
4
130
a.) By hand, determine the simple regression equation relating Y
and X.
b.) Calculate the R-Square measure and interpret the result.
c.) Calculate the adjusted R-Square.
d.) Test to see whether X and Y are significantly related using
a test on the population correlation. Test this at the 0.05
level.
e.) Test to see whether X and Y...
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X Y
2 70
0 70
4 130
Test to see whether X and Y are significantly related using a
t-test on the slope of X. Test this at the 0.05 level.
Test to see whether X and Y are significantly related using an
F-test on the slope of X. Test this at the 0.05 level.
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X
Y
2
70
0
70
4
130
a.) By hand, determine the simple regression equation relating Y
and X.
b.) Calculate the R-Square measure and interpret the result.
c.) Calculate the adjusted R-Square.
d.) Test to see whether X and Y are significantly related using
a test on the population correlation. Test this at the 0.05
level.
e.) Test to see whether X and Y...
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X Y
2 70
0 70
4 130
By hand, determine the simple regression equation relating Y
and X.
Calculate the R-Square measure and interpret the result.
Calculate the adjusted R-Square.
Test to see whether X and Y are significantly related using a
test on the population correlation. Test this at the 0.05
level.
Test to see whether X and Y are significantly related using a...
Suppose we have the following data on variable X (independent) and variable Y (dependent): X Y...
Suppose we have the following data on variable X (independent)
and variable Y (dependent):
X
Y
2
70
0
70
4
130
(SOLVE ALL BY HAND, NOT BY USING EXCEL)
By hand, determine the simple regression equation relating Y
and X.
Calculate the R-Square measure and interpret the result.
Calculate the adjusted R-Square.
Test to see whether X and Y are significantly related using a
test on the population correlation. Test this at the 0.05
level.
Test to see whether...
Suppose we have the following data on a dependent variable (Y) and an explanatory variable (X):...
Suppose we have the following data on a dependent variable (Y)
and an explanatory variable (X):
X Y
0 140
1 140
4 0
0 180
3 80
2 120
4 0
1 200
2 120
3 40
Calculate the simple linear regression equation by hand. Show
all your work. Using your result, predict the value of Y when X =
3.5. (15 points)
Calculate the R2and the adjusted
R2measures (by hand) and provide an interpretation of
what they tell us. (12 points)
Test (by hand) to see whether this is...
Suppose we have the following values on the number of customers (X) and the average profits...
Suppose we have the following values on the number of customers
(X) and the average profits (Y) for fifteen stores:
Store
Customers
(X) Average
Profits (Y)
A
161
157
B
99
93
C
135
136
D
120
123
E
164
153
F
221
241
G
179
201
H
204
206
I
214
229
J
101
135
K
231
224
L
206
195
M
248
242
N ...
Suppose we have the following values on the number of customers (X) and the average profits...
Suppose we have the following values on the number of customers
(X) and the average profits (Y) for fifteen stores:
Store
Customers
(X)
Average Profits (Y)
A
161
157
B
99
93
C
135
136
D
120
123
E
164
153
F
221
241
G
179
201
H
204
206
I
214
229
J
101
135
K
231 ...
Suppose we have a random variable X that is uniformly distributed between a = 0 and...
Suppose we have a random variable X that is uniformly
distributed between a = 0 and b = 100. What is σ X?
a. 0.913
b. 0.833
c. 50
d. 7.071
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