Q. 21 - Elementary Statistics

Question

Graduation Rates. Graduation rate-the percentage of entering freshmen attending full time and graduating within 5 years and what influences it is a concern in U.S. colleges and universities.

US News and World Report's "College Guide" provides data on graduation rates for colleges and universities as a function of the per centage of freshmen in the top 10% of their high school class, total spending per student, and student-to-faculty ratio. A random sample of 10 universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate (Grad rate).

a. Draw a scatterplot of the data.

b. Is finding a regression line for the data reasonable? Explain your answer.

c. Determine the regression equation for the data, and draw its graph

on the scatterplot you drew in part (a).

d. Describe the apparent relationship between student-to-faculty

ratio and graduation rate. 

e. What does the slope of the regression line represent in terms of student-to-faculty ratio and graduation rate?

f. Use the regression equation to predict the graduation rate of a university having a student-to-faculty ratio of 17.

g. Identify outliers and potential influential observations

Step-by-Step Solution

Answer

B ) : 

The data is reasonable to find the regression line, because the data points are appear to be

scatter about the line. 

C) : 

From the output the regression equation is

y=16.4+2.03x

D) :

From the above scatter plot the Graduation rate tends to increase as student-to-faculty ratio increases.

E ) :

The regression equation is y=16.4+2.03x.

F ): 

the graduation rate of a university having a student -to-faculty ratio of 17 is 50.91% 

Step 1. Given

Graduation rate the percentage of entering freshmen attending full time and graduating within 5 years and what influences it have become a concern in US colleges and universities A random sample of 10 universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate (Grad rate).

SF_RATIO	16	20	17	19	22	17	17	17	10	18
GRADRATE	45	55	70	50	47	46	50	66	26	60

Step 2. Part ( a )

Using MINITAB the scatterplot for the given data is shown below.

Step 3. Part ( b )

The data is reasonable to find the regression line, because the data points are appear to be

scatter about the line. 

Step 4. Part ( c )

Using MINITAB the regression output for the given data is shown below

From the output the regression equation is

y=16.4+2.03x

Using MINITAB the graph of the line y=16.4+2.03x is shown below

Step 5. Part ( d )

From the above scatter plot the Graduation rate tends to increase as student-to-faculty ratio increases.

Step 6. Part ( e )

The regression equation is y=16.4+2.03x.

Graduation rate increases by an estimated 2.03 percentage points for each increase of 1 in the student-to-faculty ratio.

Step 7. Part ( f )

To predict the graduation rate of a university having a student-to-faculty ratio of 17 is

y=16.4+2.03x. 

  =16.4+2.03(17)

   =$\boxed{50.91}$

Therefore, the graduation rate of a university having a student -to-faculty ratio of 17 is 50.91%

Step 8. Part ( g )

From part (b) we observe that the graph has no outers . The data point (10, 26) is a potential influential observation.