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 , , and . 2. The explanatory variable is and the response variable is . The summary statistics for graduation rate and median SAT score are listed below. The correlation between graduation rate and median SAT score is 0.673. Median SAT score: mean = 1038.1, standard deviation = 77.5 Graduation rate: mean = 49.4, standard deviation = 15 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 of in Graduation Rate. 5. The recorded median SAT score for Northern Michigan University is 1030. Use the regression equation to estimate the graduation rate for Northern Michigan University. 6. The recorded graduation rate for Northern Michigan University is 46.4. 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. lower than C. higher 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. Yes, because 1455 is a reasonable median SAT score for an elite university. B. No, because 103.705% is too large to be a reasonable graduation rate, even for an elite university. C. No, because 1455 is beyond the range of the data used to build the regression model.

Answer 1

Solution

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

Question cannot be addressed because scatter plot referred in the question is not attached with the question.

Answer 1

2. The explanatory variable is Median SAT score Answer 2

    response variable is . graduation rate Answer 3

3. The equation of the regression line is:

    Graduation Rate (y) = - 88.5253 + 0.1329Median SAT Score (x) Answer 4

   [Calculation details at the end]

4. An increase of one unit in Median SAT score corresponds to

    a/an increase of 0.1329 in Graduation Rate. Answer 5

5. Graduation rate for Northern Michigan University with a recorded median SAT score of 1030 is:

    48.32 Answer 6 [obtained by substituting x = 1030 in the equation under (3)]

6. The residual for Northern Michigan University is: 46.4 – 48.32 = - 1.82 Answer 7

    This means the graduation rate at Northern Michigan University is A. the same as B. lower than C. higher

    than the rate predicted by the regression model. Answer 8

7. Question cannot be addressed because scatter plot referred in the question is not attached with the

    question. Answer 9

[Going beyond: if the range of x-values in the scatter plot contains 1455 or 1455 just a bit out of the

range, the estimated regression equation can be used to estimate the graduation rate – else it cannot

   be done.]

DONE

Details of calculations

Given	n	Xbar	Ybar	SDx	SDy	rxy
	92	1038.1	49.4	77.5	15.3	0.673
β1cap = r.(SDy/SDx) = 0.132863226
β0cap = Ybar – β1cap.Xbar = - 88.5253147

Complete