The Federal Graduation Rate (FGR) for a college/university is the percentage of
ID: 2949324 • Letter: T
Question
The Federal Graduation Rate (FGR) for a college/university is the percentage of the school's admitted freshmen that graduate from that school within 6 years. A school's FGR is calculated for all students, for all athletes, and for athletes in individual sports. The FGR is especially useful in the athletic context because it enables comparison of the academic success of athletes with the academic success of other students on campus.
Evaluation of the academic success of a school's football players frequently focuses on the difference, or gap between the FGR of the student body and the FGR of the football players, calculated as gap = student body FGR?football player FGR. A large positive value for a school's gap means that the FGR of the football players is much less than the FGR of the student body.
This Excel file (https://www.webassign.net/userimages/FGR%20GAP%20webassign.xls?db=v4net&id=266817) Federal Graduation Rates shows the FGRs for 12 ACC schools and 14 SEC schools. Shown are the FGRs for football players at each school for the years 2009, 2010, 2011, and 2012, in addition to each school's football mean FGR and overall student body mean FGR over these 4 years.
The mean of the 2009, 2010, 2011, and 2012 end-of-season Sagarin Ratings of each team is included in the above file as a measure of each school's football success. The Sagarin Ratings, developed by Jeff Sagarin, apply a proprietary statistical technique to evaluate each team by taking into account several factors such as strength of schedule, strength of opponent schedules, win/loss records, wins on the road and other variables. The Sagarin ratings were obtained from USA Today, which has been publishing them since 1985.
Question 1. Make a scatterplot of the results for the 26 schools using the "Sagarin mean" as the x-variable and the "gap: all-student FGR minus football FGR" as the y-variable. Which school corresponds to the outlier in the lower right corner? Alabama
slope b1 = .2987
intercept b0 = -4.27
Question 4. Construct a 99% prediction interval for the gap at the school in Question 1. (NEED THIS ANSWER)
_______ lower bound of prediction interval (use 3 decimal places).
_______ upper bound of prediction interval (use 3 decimal places).
Explanation / Answer
Result:
Question 1. Make a scatterplot of the results for the 26 schools using the "Sagarin mean" as the x-variable and the "gap: all-student FGR minus football FGR" as the y-variable. Which school corresponds to the outlier in the lower right corner? Alabama
Question 2. With the data for the school in question 1 removed, find the slope b1 and intercept b0 of the least squares prediction line = b0 + b1x, where x is the Sagarin mean and y is the gap: all-student FGR minus football FGR.
slope b1 = .2987
intercept b0 = -4.27
Question 3a. Use the least squares prediction line = b0 + b1x from Question 2 to predict the gap for the university in Question 1. (NEED THIS ANSWER)
When x=99.53
predicted y =-4.27+0.2987*99.53
=25.45
Question 3b. What is the residual y? for the university in Question 1? (-19.95)
Question 4. Construct a 99% prediction interval for the gap at the school in Question 1. (NEED THIS ANSWER)
-3.218 lower bound of prediction interval (use 3 decimal places).
54.128 upper bound of prediction interval (use 3 decimal places).
Regression Analysis
r²
0.064
n
25
r
0.252
k
1
Std. Error
8.435
Dep. Var.
gap: all student FGR minus football FGR (y)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
111.2549
1
111.2549
1.56
.2237
Residual
1,636.5601
23
71.1548
Total
1,747.8150
24
Regression output
confidence interval
variables
coefficients
std. error
t (df=23)
p-value
99% lower
99% upper
Intercept
-4.2797
18.3513
-0.233
.8177
-55.7978
47.2384
Sagarin mean (x)
0.2987
0.2389
1.250
.2237
-0.3720
0.9694
Predicted values for: gap: all student FGR minus football FGR (y)
99% Confidence Interval
99% Prediction Interval
Sagarin mean (x)
Predicted
lower
upper
lower
upper
Leverage
99.53
25.45362
9.28973
41.61752
-3.21783
54.12507
0.466
Regression Analysis
r²
0.064
n
25
r
0.252
k
1
Std. Error
8.435
Dep. Var.
gap: all student FGR minus football FGR (y)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
111.2549
1
111.2549
1.56
.2237
Residual
1,636.5601
23
71.1548
Total
1,747.8150
24
Regression output
confidence interval
variables
coefficients
std. error
t (df=23)
p-value
99% lower
99% upper
Intercept
-4.2797
18.3513
-0.233
.8177
-55.7978
47.2384
Sagarin mean (x)
0.2987
0.2389
1.250
.2237
-0.3720
0.9694
Predicted values for: gap: all student FGR minus football FGR (y)
99% Confidence Interval
99% Prediction Interval
Sagarin mean (x)
Predicted
lower
upper
lower
upper
Leverage
99.53
25.45362
9.28973
41.61752
-3.21783
54.12507
0.466
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