One way colleges measure success is by graduation rates. Let us investigate some variables that contribute to this statistic for medium and large colleges in the United States by developing a useful linear regression model to describe the relationship between the 2016 6-year graduation rate and four variables. One possible model that will be considered is y=x+B₁x₁ + B₂x₂ + B₂x3+B₂X4+e where y is the 2016 6-year graduation rate, x, is the average high school GPA among college freshmen, x₂ is the estimated median SAT among college freshmen, x₂ is the full-time undergraduate student-to-faculty ratio, x is the percentage of Pell Grant recipients among freshmen, and e is the random deviation associated with each value of y. The random deviations are assumed to be normally distributed with a mean value of 0 and constant variance of ². Step 1: When developing a linear regression model, scatterplots of y with each potential predictor can help determine whether the relationship among the variables is linear or nonlinear. Create the four scatterplots of y against each x predictor. Upload a scatterplot for each pair as indicated below. Scatterplot of y against average freshman high school GPA. (Submit a file with a maximum size of 1 MB.)
One way colleges measure success is by graduation rates. Let us investigate some variables that contribute to this statistic for medium and large colleges in the United States by developing a useful linear regression model to describe the relationship between the 2016 6-year graduation rate and four variables. One possible model that will be considered is y=x+B₁x₁ + B₂x₂ + B₂x3+B₂X4+e where y is the 2016 6-year graduation rate, x, is the average high school GPA among college freshmen, x₂ is the estimated median SAT among college freshmen, x₂ is the full-time undergraduate student-to-faculty ratio, x is the percentage of Pell Grant recipients among freshmen, and e is the random deviation associated with each value of y. The random deviations are assumed to be normally distributed with a mean value of 0 and constant variance of ². Step 1: When developing a linear regression model, scatterplots of y with each potential predictor can help determine whether the relationship among the variables is linear or nonlinear. Create the four scatterplots of y against each x predictor. Upload a scatterplot for each pair as indicated below. Scatterplot of y against average freshman high school GPA. (Submit a file with a maximum size of 1 MB.)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:GradRate_2016
0.917
0.872
0.724
0.706
0.675
0.865
0.764
0.743
0.501
0.939
0.832
0.82
0.789
0.645
0.598
0.581
0.316
0.701
0.582
0.509
0.466
0.434
0.362
0.6
0.548
0.528
0.456
0.303
0.413
0.374
GPA_Avg
3.87
3.94
3.79
3.62
3.62
3.6
3.64
3.5
3.18
3.95
3.75
3.97
3.69
3.61
3.32
3.49
2.93
3.49
3.5
3.08
3.37
3.32
3.2
3.5
3.2
3.36
3.26
3.12
3.4
3.29
SAT_Med
1397
1175
1271
1081
1204
1303
1199
1142
902
1479
1222
1211
1217
1086
960
1080
962
1072
1067
990
1088
1069
993
1110
951
1131
990
961
1029
992
Perc Freshmen__
Pell
0.23
0.409
0.333
0.256
0.199
0.133
0.188
0.193
0.632
0.135
0.185
0.074
0.145
0.283
0.441
0.433
0.679
0.234
0.281
0.494
0.319
0.36
0.479
0.512
0.366
0.224
0.536
0.488
0.385
0.515
Ratio
9
11
9
19
12
5
13
13
32
2
11
14
14
34
20
18
65
19
8
19
17
13
15
19
19
18
28
16
23
13
Transcribed Image Text:One way colleges measure success is by graduation rates. Let us investigate some variables that contribute to this statistic for medium and large
colleges in the United States by developing a useful linear regression model to describe the relationship between the 2016 6-year graduation rate and
four variables.
One possible model that will be considered is
y=x+B₁x₁ + B₂X₂ + B3X3 + B4X4+e
where y is the 2016 6-year graduation rate, x, is the average high school GPA among college freshmen, x₂ is the estimated median SAT among
college freshmen, x3 is the full-time undergraduate student-to-faculty ratio, x is the percentage of Pell Grant recipients among freshmen, and e is the
random deviation associated with each value of y. The random deviations are assumed to be normally distributed with a mean value of 0 and
constant variance of 2,
Step 1: When developing a linear regression model, scatterplots of y with each potential predictor can help determine whether the relationship among
the variables is linear or nonlinear. Create the four scatterplots of y against each x predictor. Upload a scatterplot for each pair as indicated below.
Scatterplot of y against average freshman high school GPA. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
This answer has not been graded yet.
Is it reasonable to consider the relationship shown in the graph as linear?
O Yes, the scatterplot does not show a linear pattern and/or there is at least one outlier.
Yes, the scatterplot shows a linear pattern with no outliers.
O No, the scatterplot does not show a linear pattern and/or there is at least one outlier.
No, the scatterplot shows a linear pattern with no outliers.
Scatterplot of y against estimated median SAT among college freshmen. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
This answer has not been graded yet.
Is it reasonable to consider the relationship shown in the graph as linear?
OYes, the scatterplot does not show a linear pattern and/or there is at least one outlier.
Yes, the scatterplot shows a linear pattern with no outliers.
O No, the scatterplot does not show a linear pattern and/or there is at least one outlier.
O No, the scatterplot shows a linear pattern with no outliers.
Scatterplot of y against full-time undergraduate student-to-faculty ratio. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
This answer has not been graded yet.
Is it reasonable to consider the relationship shown in the graph as linear?
Yes, the scatterplot does not show a linear pattern and/or there is at least one outlier.
OYes, the scatterplot shows a linear pattern with no outliers.
No, the scatterplot does not show a linear pattern and/or there is at least one outlier.
O No, the scatterplot shows a linear pattern with no outliers.
Scatterplot of y against percentage of Pell Grant recipients among freshmen. (Submit a file with a maximum size of 1 MB.)
Choose File No file chosen
This answer has not been graded yet.
Is it reasonable to consider the relationship shown in the graph as linear?
OYes, the scatterplot does not show a linear pattern and/or there is at least one outlier.
Yes, the scatterplot shows a linear pattern with no outliers.
O No, the scatterplot does not show a linear pattern and/or there is at least one outlier.
O No, the scatterplot shows a linear pattern with no outliers.
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