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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

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

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...
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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
Create a simple linear regression model that predicts the 2016 6-year graduation rate with average high school GPA among college freshmen. The model under consideration is y = x + B₁x₁ + e where y is the 2016 6-year graduation rate, x₁ is the average high school GPA among college 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. Create a simple linear regression model to predict the 2016 6-year graduation rate using only the average high school GPA among college freshmen. Let the significance level be x = 0.05. Save the standardized residuals from the analysis so that the assumption on the random deviation, e, can be verified with a normal probability plot. To create a normal probability plot, also known as a Q-Q plot, of the standardized residuals, you will need the normal_scores.csv file that contains normal scores for a n = 30 sample. Save the Standardized Residuals from the analysis, sort them in ascending order from the output and pair them with the normal scores from the document to form (normal percentile, Standardized Residuals) ordered pairs for the normal probability plot. Create and upload a normal probability plot. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. Does the plot indicate that the assumption of normality and constant variance, o², of the random deviation, e, distribution is reasonable? Yes, the plot is quite straight. No, the plot is not straight. What is the F statistic from the analysis? (Round your answer to one decimal place.) According to the P-value associated with this test statistic, this test confirms the usefulness of this model with only one predictor. Provide the linear multiple regression model. (Round your answers to three decimal places.) 2016 6-year graduation rate = GPA Step 7: What is the value of R2 from the analysis? (Round your answer to one decimal place.) % What is the estimated random error standard deviation? (Round your answer to three decimal places.) SSResid n - (k+1) Se = Compare the two values of R² for the two regression models. The R² for the model with three predictors is close to The s for the model with three predictors is close to This suggests that average high school GPA among college freshman explains [about the same graduation rate in 2016 as all three variables together, and so the simpler model is preferred independent variables. the R² for the model with one predictor. the so for the model with one predictor. amount of variability in 6-year over the more complicated model with three
Transcribed Image Text:Create a simple linear regression model that predicts the 2016 6-year graduation rate with average high school GPA among college freshmen. The model under consideration is y = x + B₁x₁ + e where y is the 2016 6-year graduation rate, x₁ is the average high school GPA among college 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. Create a simple linear regression model to predict the 2016 6-year graduation rate using only the average high school GPA among college freshmen. Let the significance level be x = 0.05. Save the standardized residuals from the analysis so that the assumption on the random deviation, e, can be verified with a normal probability plot. To create a normal probability plot, also known as a Q-Q plot, of the standardized residuals, you will need the normal_scores.csv file that contains normal scores for a n = 30 sample. Save the Standardized Residuals from the analysis, sort them in ascending order from the output and pair them with the normal scores from the document to form (normal percentile, Standardized Residuals) ordered pairs for the normal probability plot. Create and upload a normal probability plot. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. Does the plot indicate that the assumption of normality and constant variance, o², of the random deviation, e, distribution is reasonable? Yes, the plot is quite straight. No, the plot is not straight. What is the F statistic from the analysis? (Round your answer to one decimal place.) According to the P-value associated with this test statistic, this test confirms the usefulness of this model with only one predictor. Provide the linear multiple regression model. (Round your answers to three decimal places.) 2016 6-year graduation rate = GPA Step 7: What is the value of R2 from the analysis? (Round your answer to one decimal place.) % What is the estimated random error standard deviation? (Round your answer to three decimal places.) SSResid n - (k+1) Se = Compare the two values of R² for the two regression models. The R² for the model with three predictors is close to The s for the model with three predictors is close to This suggests that average high school GPA among college freshman explains [about the same graduation rate in 2016 as all three variables together, and so the simpler model is preferred independent variables. the R² for the model with one predictor. the so for the model with one predictor. amount of variability in 6-year over the more complicated model with three
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