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 0.641.

Median SAT score: mean = 1029.1, standard deviation = 78.3
Graduation rate: mean = 49.2, standard deviation = 14.7

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 1028. Use the regression equation to estimate the graduation rate for Northern Michigan University.  

6. The recorded graduation rate for Northern Michigan University is 47.9. Complete the following sentence.

The residual for Northern Michigan University is  . This means the graduation rate at Northern Michigan University is
A. the same as
B. higher than
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 100.453% is too large to be a reasonable graduation rate, even for an elite university.
B. No, because 1455 is beyond the range of the data used to build the regression model.
C. Yes, because 1455 is a reasonable median SAT score for an elite university.

Answer 1

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

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

The correlation between graduation rate and median SAT score, r =  0.641.

Median SAT score: mean, x̅ = 1029.1, standard deviation, sx = 78.3

Graduation rate: mean, y̅ = 49.2, standard deviation, sy = 14.7

3.

Slope, b = r*sy/sx = 0.641*14.7/78.3 = 0.12034

Intercept, a = y̅ - b* x̅ = 49.2 - (0.12034)*1029.1 = -74.6429

Regression equation :   

ŷ = -74.6429 + (0.1203) 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 increase of 0.1203 in Graduation Rate.

5. The recorded median SAT score for Northern Michigan University is 1028. Use the regression equation to estimate the graduation rate for Northern Michigan University.  

Predicted value of y at x = 1028

ŷ = -74.6429 + (0.1203) * 1028 = 49.0676

6. The recorded graduation rate for Northern Michigan University is 47.9.

Residual = y - ŷ = 47.9 - 49.0676 = -1.1676

The residual for Northern Michigan University is -1.1676.

This means the graduation rate at Northern Michigan University is C. lower than the rate predicted by the regression model.

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