Create a Scatterplot of y against estimated median SAT among college freshmen. GradRate 2016 GPA_Avg SAT_Med Perc_Freshmen_Pell Ratio0.9170.8720.7240.7060.6750.8650.7640.7430.5010.9390.8320.820.7890.6450.5980.5810.3160.7010.5820.5090.4660.4340.3620.60.5480.5280.4560.3030.4130.3743.873.943.793.623.623.63.643.53.183.953.753.973.693.613.323.492.933.493.53.083.373.323.23.53.23.363.263.123.43.291397117512711081120413031199114290214791222121112171086960108096210721067990108810699931110951113199096110299920.230.4090.3330.2560.1990.1330.1880.1930.6320.1350.1850.0740.1450.2830.4410.4330.6790.2340.2810.4940.3190.360.4790.5120.3660.2240.5360.4880.3850.5159119191251313322111414342018651981917131519191828162313 One way colleges measure success is by graduation rates. Let us investigate some variables that contributeto this statistic for medium and large colleges in the United States by developing a useful linear regressionmodel to describe the relationship between the 2016 6-year graduation rate and four variables.One possible model that will be considered isy = x + ₁x₁ + ₂x₂ + B3x3 + 4x4 + ewhere y is the 2016 6-year graduation rate, x₁ is the average high school GPA among college freshmen, X2is the estimated median SAT among college freshmen, x3 is the full-time undergraduate student-to-facultyratio, x is the percentage of Pell Grant recipients among freshmen, and e is the random deviationassociated with each value of y. The random deviations are assumed to be normally distributed with a meanvalue of 0 and constant variance of o².

Here, we have given the data for 2016 graduation rate and full-time undergraduate student to faculty…

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Create a Scatterplot of y against estimated median SAT among college freshmen.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 11MCQ

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Question

Create a Scatterplot of y against estimated median SAT among college freshmen.

GradRate 2016 GPA_Avg SAT_Med Perc_Freshmen_Pell Ratio
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
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
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
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
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

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 + ₁x₁ + ₂x₂ + B3x3 + 4x4 + e
where y is the 2016 6-year graduation rate, x₁ 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 o².

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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