辅导ADA2留学生、讲解Python、c++、Java编程语言、讲解ACT test

ADA2:

Assignment 1: Due 01/31/2019 Thursday in class

The director of admissions of a small college selected 120 students at random from

the new freshman class in a study to determine whether a student’s grade point average

(GPA) at the end of the freshman year (Y ) can be predicted from students’ ACT test

score (test-score), IQ score (IQ), and high school average score (HS-Avg).

ex.data<-read.table("http://www.math.unm.edu/~luyan/ADA219/gpa.txt",header=T)

1. Plot scatter plot matrix, correlation matrix of Y and predictors, and briefly comment

on them.

2. Fit a multiple regression model with the three predictors IQ, HS-Avg and test-score.

State model assumptions and the fitted regression model.

3. Evaluate model assumptions using appropriate plots and tests.

4. Are there any outlying residuals in this data set? Are there any outliers in any of

the predictor variables? If so which observation(s) and which predictor? Explain

how this observation can be a fairly extreme outlier in terms of its x value but still

not produce an outlying ei value.

Let’s continue with the following problems even if the model above is

inappropriate

5. Conduct statistical tests to determine the importance of each predictor variable.

State hypotheses, p-values, and decisions. What do you conclude?

6. What is the multiple coefficient of determination? Interpret.

7. Obtain 95% CI for expected freshman GPA for a student with test score= 32, IQ

= 82, HS-Avg= 72. Interpret.

8. Frank Buffay obtained a score of 32 on the test-score. He also has IQ = 82, HSAvg=

72. Predict his freshman GPA using a 95% prediction interval. Interpret your

prediction interval.

1

9. Consider the linear regression model with GPA as the response and test score (X1),

IQ (X2), and HSAvg (X3) as the predictors.

Fit the model with X1 as the only predictor. Then fit the model Y = β0 + β1X1 +

β2X2 +  (you can use results from (b)). Comment on the tests on β1 in these two

models. How do you explain the difference?

10. Now try a transformation on Y , and evaluate model assumptions.