Question

(1 point) 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 0.676.

Median SAT score: mean = 1038.5, standard deviation = 78.6
Graduation rate: mean = 48.2, standard deviation = 13.4

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 48.1. 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 96.200% 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. The relationship between SAT score and graduation rate is linear, strong and positive ( Please check the options for the correct answers).

2. Explantory variable = Median SAT
response variable = Graduation rate

3. Regression equation give below.

4.
An increase of 1 unit in Median SAT Score corresponds to an increase of 0.115 in Graduation Rate.

5. Predicted graduation rate is given below.

6.

Residual = actual - Predicted = 48.1-47.4525 = 0.6475

It is higher than the predicted

7. A value upto 2 std. Deviation from the mean can be considered for the model. A value beyond that would not give a correct result.

1455 is beyond the 2std. Deviation limit of the mean values seen by the model hence it cannot be used.

correct answer: C. No because 1455 is beyond the range of the data used to build the regression model.