Question
In: Statistics and Probability
Consider a binary response variable y and an explanatory variable x. The following table contains the...
Consider a binary response variable y and an explanatory variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logit model, with the associated p-values shown in parentheses.
| Variable | LPM | Logit | |||
| Constant | −0.78 | −5.90 | |||
| (0.03 | ) | (0.03 | ) | ||
| x | 0.04 | 0.28 | |||
| (0.07 | ) | (0.02 | ) | ||
a. Test for the significance of the intercept and
the slope coefficients at the 5% level in both models.
| Coefficients | LPM | Logit | |||
| Intercept | |||||
| Slope | |||||
b. What is the predicted probability implied by
the linear probability model for x = 24 and x =
31? (Round intermediate calculations to at least 4 decimal
places and final answers to 2 decimal places.)
| y-hat | |||||
| x=24 | |||||
| x=31 | |||||
c. What is the predicted probability implied by
the logit model for x = 24 and x = 31?
(Round intermediate calculations to at least 4 decimal
places and final answers to 2 decimal places.)
| y-hat | |||||
| x=24 | |||||
| x=31 | |||||
Solutions
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orchestra answered 2 years agoRelated Solutions
Consider a binary response variable y and an explanatory variable x. The following table contains the...
Consider a binary response variable y and an
explanatory variable x. The following table contains the
parameter estimates of the linear probability model (LPM) and the
logit model, with the associated p-values shown in
parentheses.
Variable
LPM
Logit
Constant
−0.70
−6.60
(0.03
)
(0.03
)
x
0.04
0.18
(0.04
)
(0.03
)
a. Test for the significance of the intercept and
the slope coefficients at the 5% level in both models.
coefficient
LPM
Logit
intercept
slope
b. What is the...
17.3 Consider a binary response variable y and an explanatory variable x. The following table contains...
17.3
Consider a binary response variable y and an
explanatory variable x. The following table contains the
parameter estimates of the linear probability model (LPM) and the
logit model, with the associated p-values shown in
parentheses.
Variable
LPM
Logit
Constant
−0.69
−6.30
(0.04)
(0.06)
x
0.05
0.15
(0.07)
(0.06)
a.
Test for the significance of the intercept and the slope
coefficients at a 5% level in both models.
Coefficients
LPM
Logit...
Consider a binary response variable y and two explanatory variables x1 and x2. The following table...
Consider a binary response variable y and two
explanatory variables x1 and
x2. The following table contains the parameter
estimates of the linear probability model (LPM) and the logit
model, with the associated p-values shown in
parentheses.
Variable
LPM
Logit
Constant
−0.40
−2.20
(0.03
)
(0.01
)
x1
0.32
0.98
(0.04
)
(0.06
)
x2
−0.04
−0.20
(0.01
)
(0.01
)
a. At the 5% significance level, comment on the
significance of the variables for both models.
Variable
LPM
Logit...
Consider data regarding a response y and an explanatory variable x, both numeric x y 1...
Consider data regarding a response y and an explanatory variable
x, both numeric
x
y
1
2.8
0.7
2
2.6
1.3
3
6.8
-1.1
4
3.0
0.2
5
4.7
1.1
6
5.0
-0.1
7
5.0
0.9
8
2.9
1.0
9
7.0
-0.2
10
3.7
0.8
The null hypothesis that the expected value of the response is
constant for all values of the explanatory variable is:
Select one:
a. Not rejected with a significance level of 5%.
b. Rejected with a...
a)By hand, draw a scatter diagram treating x as the explanatory variable and y as the response variable
x
4
5
6
8
9
y
6
8
11
14
16
a)By hand, draw a scatter diagram treating x as the explanatory
variable and y as the response variable
b)Find the equation of the line containing the points (44,66)
and (9,16).
c)Graph the line found in part (b) on the scatter diagram.
d)By hand, determine the least-squares regression line.
e)Graph the least-squares regression line on the scatter
diagram.
f)Compute the sum of the squared residuals for the line found...
Collect data on one response (dependent or y) variable and two different explanatory (independent or x)...
Collect data on one response (dependent or y) variable and two
different explanatory (independent or x) variables. This will
require a survey with three questions. For example: To predict a
student’s GPA (y), you might collect data on two x variables: SAT
score and age. So we would be trying to determine if there was a
linear correlation between someone’s SAT score and their GPA, as
well as their age and their GPA. (Note: students may not choose GPA
as...
Collect data on one response (dependent or y) variable and two different explanatory (independent or x)...
Collect data on one response (dependent or y) variable and two
different explanatory (independent or x) variables. This will
require a survey with three questions. For example: To predict a
student’s GPA (y), you might collect data on two x variables: SAT
score and age. So we would be trying to determine if there was a
linear correlation between someone’s SAT score and their GPA, as
well as their age and their GPA. (Note: students may not choose GPA
as...
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...
A two-variable model involving one quantitative explanatory variable and one categorical (binary) explanatory variable (and no...
A two-variable model involving one quantitative explanatory
variable and one categorical (binary) explanatory variable (and no
interaction), results in two regression lines that are:
A. Always parallel.
B. Could be parallel but, depending
on the data, may not.
C. Never parallel.
D. Always horizontal.
The two methods of including a binary categorical variable in a
regression model are to use indicator coding or effect coding. For
indicator coding in the two-variable model (with
no interaction):
A. The binary variable is coded
(-1,1) and the coefficient...
b) In the following examples, identify the response variable and the explanatory variables illustrating their levels...
b) In the following examples, identify the response variable and
the explanatory variables illustrating their levels of
measuremsnt
i) Marital status (married, single, divorced,
widowed), Quality of life (excellent, good, fair, poor).
ii) presence of a disease( Presnet, Absent) , gender ( male,
Female),
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