Question
In: Statistics and Probability
Estimate: GPA = β0 + β1GRE + ε, where GRE is a student’s score on the...
Estimate: GPA = β0 + β1GRE + ε, where GRE is a student’s score on the math portion of the Graduate Record Examination (GRE) score and GPA is the student’s grade point average in graduate school. [You may find it useful to reference the t table.]
| GPA | GRE |
| 2.8 | 750 |
| 3.4 | 670 |
| 2.5 | 780 |
| 3.4 | 680 |
| 2.8 | 720 |
| 3.7 | 770 |
| 2.4 | 750 |
| 2.6 | 760 |
| 3.8 | 680 |
| 2.7 | 740 |
| 2.7 | 680 |
| 3.1 | 640 |
| 3 | 710 |
| 2.6 | 710 |
| 3.2 | 700 |
| 3.5 | 750 |
| 3.9 | 700 |
| 2.5 | 660 |
| 2.9 | 740 |
| 3.5 | 660 |
| 2.1 | 760 |
| 2.7 | 660 |
| 3.8 | 650 |
| 2.5 | 670 |
a. Construct the 90% confidence interval for the
expected GPA for an individual who scored 730 on the math portion
of the GRE. (Round regression estimates to at least 4
decimal places, "tα/2,df"
value to 3 decimal places, and final answers to 2 decimal
places.)
b. Construct the 90% prediction interval for GPA
for an individual who scored 730 on the math portion of the GRE.
(Round regression estimates to at least 4 decimal places,
"tα/2,df" value to 3
decimal places, and final answers to 2 decimal
places.)
Solutions
orchestra answered 2 years agoRelated Solutions
Estimate: GPA = β0 + β1GRE + ε, where GRE is a student’s score on the...
Estimate: GPA = β0 + β1GRE + ε, where GRE is a student’s score
on the math portion of the Graduate Record Examination (GRE) score
and GPA is the student’s grade point average in graduate school.
[You may find it useful to reference the t table.] picture
GPA
GRE
3.3
760
3.8
680
3
670
3.2
710
3.8
780
2.6
680
2.5
760
2.4
670
2.8
640
3.9
700
3.8
680
3.4
680
2.8
760
3.1
650
3.4
670
2.7...
You are given the following data, where X1 (GRE total score) and X2 (undergraduate GPA) are...
You are given the following data, where X1 (GRE total score) and
X2 (undergraduate GPA) are used to predict Y (graduate GPA):
Y
X1 X2
3.6
135
2.6
4
130
2.6
3
105
2.4
3.3
115
2.7
3.2
105
3.1
3
100
3.2
2.7
110
3.8
3.8
125
3.6
4
145
3.2
Determine the following multiple regression values.
Report intercept and slopes for regression equation accurate to 3
decimal places:
Intercept: a=
Partial slope X1: b1=
Partial...
Data shows graduate program admission decisions (Yes: 1 and No: 2), GRE score and undergraduate GPA...
Data shows graduate program admission decisions (Yes: 1 and No:
2), GRE score and undergraduate GPA for twenty-five students.
Tasks:
Examine if the given data is suitable for the application of
linear discriminant analysis.
Create a linear discriminant function predicting admission
decisions.
Comment on the classification accuracy.
Predict the admission decision given GRE score = 690 and GPA =
3.2.
Perform logistic regression analysis for the data.
Compare the classification accuracies of both methods.
Admit
GRE
GPA
2
790
3.8...
Where SAT is the student’s SAT score, Athlete is a dummy variable for if they were...
Where SAT is the student’s SAT score, Athlete is a dummy
variable for if they were a college athlete, High School Rank is
their ranking in their high school (1 being the highest), Female
being a dummy variable for if they are female, and Total Cred
Credit Hours being the total credit hours taken in
college. GPA measures the student’s GPA in college.
Answer the following questions and upload ALL of your work in
either a word document, or picture. ...
You decide to study the effect of GRE preparatory course on GRE score. Describe, in detail,...
You decide to study the effect of GRE preparatory course on GRE
score. Describe, in detail, how you will design your study, how you
will collect data, and how you are going to statistically test
whether the GRE course had an effect on GRE score. Be as specific
as you can about your hypotheses. How would you, if at all, change
your study if you decided to study the effect of the GRE
preparatory course on graduate school admission instead?
Fit a binary logistic regression model with admission decision as the dependent variable, GRE and GPA...
Fit a binary logistic regression model with admission decision
as the dependent variable, GRE and GPA as the independent
variables.
Evaluate the goodness of fit of the model.
Determine the significance of independent variables.
Interpret odds ratios for independent variables.
State the binary logistic regression equation.
Evaluate the classification accuracy of the model.
Check if the residuals are independent.
Admit
GRE
GPA
0
790
1
1
370
0
1
480
1
1
580
1
1
620
1
0
740
0...
The average GRE score at the University of Pennsylvania for the incoming class of 2016-2017 was...
The average GRE score at the University of Pennsylvania for the
incoming class of 2016-2017 was 311. Assume that the standard
deviation was 13.4. If you select a random sample of 40 students,
what is the probability that the sample mean will be less than 313?
Round your answer to three decimal places.
The average GRE score at the University of Pennsylvania for the
incoming class of 2016-2017 was 311. Assume that the standard
deviation was 13.4. If you select...
The statistics department is interested in the different factors that might influence a student’s score on...
The statistics department is interested in the different factors
that might influence a student’s score on the final exam. They
identify three factors to test: the student’s midterm exam score,
the number of hours the student reports having studied for the
final exam, and the average number of drinks of alcohol the student
reports having on a night out. They collect data on all of these
factors and want to estimate the following model:
FinalExamScore=β0+β1 MidtermExamScore +β2HourStudied
+β3AverageAlcohol +ε
Variable...
The data below provides College GPA, High School GPA, SAT total score, and a number of...
The data below provides College GPA, High School GPA, SAT total
score, and a number of letters of reference. a.Generate a model for
college GPA as a function of the other three variables? b.Is this
model useful? Justify your conclusion. c.Are any of the variables
not useful predictors? Why? CGPA HSGPA SAT REF 2.04 2.01 1070 5
2.56 3.4 1254 6 3.75 3.68 1466 6 1.1 1.54 706 4 3 3.32 1160 5 0.05
0.33 756 3 1.38 0.36 1058...
Consider the constant-elasticity demand function Q = p−ε, where ε > 0. Solve for the inverse...
Consider the constant-elasticity demand function Q = p−ε, where
ε > 0.
Solve for the inverse demand function p(Q).
Calculate the demand price elasticity.
Show that p(Q)/MR(Q) is independent of the output level Q.
(Hint: Use the relationship between marginal revenue and the
elasticity of demand.)
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