Question

In: Statistics and Probability

14-60. Referring to Exercise 14-58, suppose a student has an SAT score of 400. What is...

14-60.

Referring to Exercise 14-58, suppose a student has an SAT score of 400. What is her estimate GPA at State University? Discuss the ramifications of using the model developed in Exercise 14-58 to estimate this student’s GPA.

14-58

At State University, a study was done to establish whether a relationship exists between students’ graduating grade point average (GPA) and the SAT verbal score when the student originally entered the university. The sample data are reported as follows:

GPA    2.5 3.2 3.5 2.8 3.0 2.4 3.4 2.9 2.7 3.8

SAT    640 700 550 540 620 490 710 600 505 710

a. Develop a scatter plot for these data and describe what, if any, relationship exists between the two variables, GPA and SAT score.

b. (1) Compute the correlation coefficient. (2) Does it appear that the success of students at State University is related to the SAT verbal scores of those students? Conduct a statistical procedure to answer this question. Use a significance level of 0.01.

c. (1) Compute the regression equation based on these sample data if you wish to predict the university GPA using the student SAT score. (2) Interpret the regression coefficients.

Solutions

Expert Solution

Result:

problem 14-60 answered.

Referring to Exercise 14-58, suppose a student has an SAT score of 400. What is her estimate GPA at State University? Discuss the ramifications of using the model developed in Exercise 14-58 to estimate this student’s GPA.

The regression line is

GPA = 0.9772+0.0034*SAT

When SAT = 400, the predicted GPA = 0.9772+0.0034*400

=2.3372

The model is not appropriate to predict GPA when the SAT score is 400, because the value 400 is not within the range of the given SAT scores.

14-58

At State University, a study was done to establish whether a relationship exists between students’ graduating grade point average (GPA) and the SAT verbal score when the student originally entered the university. The sample data are reported as follows:

GPA    2.5 3.2 3.5 2.8 3.0 2.4 3.4 2.9 2.7 3.8

SAT    640 700 550 540 620 490 710 600 505 710

a. Develop a scatter plot for these data and describe what, if any, relationship exists between the two variables, GPA and SAT score.

b. (1) Compute the correlation coefficient. (2) Does it appear that the success of students at State University is related to the SAT verbal scores of those students? Conduct a statistical procedure to answer this question. Use a significance level of 0.01.

c. (1) Compute the regression equation based on these sample data if you wish to predict the university GPA using the student SAT score. (2) Interpret the regression coefficients.

Regression Analysis

0.389

n

10

r

0.624

k

1

Std. Error

0.374

Dep. Var.

GPA

ANOVA table

Source

SS

df

MS

F

p-value

Regression

0.7147

1  

0.7147

5.10

.0539

Residual

1.1213

8  

0.1402

Total

1.8360

9  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=8)

p-value

95% lower

95% upper

Intercept

0.9772

0.9123

1.071

.3154

-1.1266

3.0811

SAT

0.0034

0.0015

2.258

.0539

-0.0001

0.0068


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