Question

College Graduation Rates. Data from the College Results Online website compared the 2011 graduation rate and median SAT score for 92 similar-sized public universities and colleges in the United States. The scatterplot below shows the relationship between these two variables along with the least squares fit. Round all calculated results to 4 decimal places.

1. The relationship between median SAT score and graduation rate is  ? positive negative ,  ? weak strong , and  ? linear non-linear .

2. The explanatory variable is  ? graduation rate median SAT college year  and the response variable is  ? graduation rate median SAT college year .

The summary statistics for graduation rate and median SAT score are listed below. The correlation between graduation rate and median SAT score is 0.655.

Median SAT score: mean = 1035.9, standard deviation = 79.3
Graduation rate: mean = 51.9, standard deviation = 14.5

3. The equation of the regression line is y =  +  x

4. Complete the following sentence to interpret the slope of the regression line:

An increase of  in Median SAT score corresponds to a/an  ? decrease increase  of  in Graduation Rate.

5. The recorded median SAT score for Northern Michigan University is 1032. Use the regression equation to estimate the graduation rate for Northern Michigan University.

6. The recorded graduation rate for Northern Michigan University is 47. Complete the following sentence.

The residual for Northern Michigan University is  . This means the graduation rate at Northern Michigan University is
A. higher than
B. the same as
C. lower than
the rate predicted by the regression model.

7. Stanford University (an elite private university in California not included in this data set) has a median SAT score of 1455. Would it be appropriate to use this linear model to predict the graduation rate for Stanford?

A. No, because 102.094% is too large to be a reasonable graduation rate, even for an elite university.
B. Yes, because 1455 is a reasonable median SAT score for an elite university.
C. No, because 1455 is beyond the range of the data used to build the regression model.

Answer 1

1.

We have given that the correlation between graduation rate and the median SAT score is 0.655. From this, we can say,

The relationship between median SAT score and the graduation rate is positive, strong and linear.

2.

The explanatory variable is the median SAT score and the response variable is graduation rate.

3.

We have,

4.

An increase of 1 median SAT score corresponds to an increase of 0.119767 in the graduation rate.

5.

Consider, x = 1030 which is the median SAT score for Northern Michigan University

Put the above value in the regression equation to get estimated graduation rate for the same university.

The estimated graduation rate for Northern Michigan University = 51.19338.

6.

The recorded graduation rate for Northern Michigan University is 47.

Residual = Actual graduation rate - Predicted graduation rate

Residual = 47 - 51.19338

Residual = -4.19338

The graduation rate for Northern Michigan University is lower than the rate predicted by the regression model.

7.

The value of the median SAT score of Stanford University 1455 is much larger than the data range.

No, because 1455 is beyond the range of the data used to build the regression model.