Homework Help is Here – Start Your Trial Now!
Math
Probability
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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question
100%
I appreciate help I can receive on this
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: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
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.
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.
Expert Solution
steps

Step by step

Solved in 5 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer