The director of college admissions at a local university is trying to determine whether a student's high school GPA or SAT score is a better predictor of the student's subsequent college GPA. She formulates two models: Model 1. College GPA = β0 + β1 High School GPA + ε Model 2. College GPA = β0 + β1 SAT Score + ε. She estimates these models using data from a sample of 10 recent college graduates. A portion of the results are as follows: ANOVA Results for Model 1 df SS MS F Significance F Regression 1 1.4415 1.4415 11.5032 0.0095 Residual 8 1.0025 0.1253 Total 9 2.4440 ANOVA Results for Model 2 df SS MS F Significance F Regression 1 1.0699 1.0699 6.2288 0.0372 Residual 8 1.3741 0.1718 Total 9 2.4440 a. Calculate the standard error of the estimate for Model 1 and Model 2. (Round your answers to 4 decimal places.) Standard error Model 1 Model 2 b. Calculate the coefficient of determination for Model 1 and Model 2. (Round your answers to 4 decimal places.) Coefficient of determination Model 1 Model 2 c. Given these two measures, which model is a better fit? provides a better fit. It has an error of the estimate and a coefficient of determination.
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Step 1
To calculate the standard error of the estimate for Model 1 and Model 2, we need to use the following formula: Standard error of the estimate = √(Residual sum of squares / degrees of freedom) For Model 1: Residual sum of squares = 1.0025 Degrees of freedom = Show more…
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A university administrator wants to use high school GPA to predict scores on an entrance exam and has the following data. Use these data to calculate the coefficient of determination, standard error of the regression, standard error of the slope and calculated t statistic from a hypothesis test on the slope where the null states the population slope = 0. GPA | Score 1.59 | 207 1.71 | 213 3.85 | 289 3.54 | 309 2.05 | 216 3.79 | 359 1.14 | 196 2.19 | 327 coefficient of determination = 0.6550, standard error of reg = 14.1468, standard error of slope = 40.4265, calculated t = 1.9432 coefficient of determination = 0.6550, standard error of reg = 9,805.7920, standard error of slope = 40.4265, calculated t = 1.9432 coefficient of determination = 0.6550, standard error of reg = 40.4265, standard error of slope = 14.1468, calculated t = 3.3749 coefficient of determination = 0.8093, standard error of reg = 40.4265, standard error of slope = 14.1468, calculated t = 3.3749 coefficient of determination = 0.8093, standard error of reg = 40.4265, standard error of slope = 9,805.7920, calculated t = 3.3749
Adi S.
The director of college admissions at a local university is trying to determine whether a student's high school GPA or SAT score is a better predictor of the student's subsequent college GPA. She formulates two models: Model 1: College GPA = β₀ + β‑High School GPA + ε Model 2: College GPA = β₀ + β‑SAT Score + ε She estimates these models and obtains the following goodness-of-fit measures. Model 1 Model 2 R² 0.5595 0.5322 Adjusted R² 0.5573 0.5298 Se 40.3684 41.6007 Which model provides a better fit for y? Model 1 since it has a smaller standard error of the estimate and a higher coefficient of determination. Model 1 since it has a higher standard error of the estimate and a smaller coefficient of determination. Model 2 since it has a smaller standard error of the estimate and a higher coefficient of determination. Model 2 since it has a higher standard error of the estimate and a smaller coefficient of determination.
Researchers try to predict students' SAT scores from their ACT (American College Testing) scores. The regression equation to be estimated in this research is: y = a + bx where y is the SAT score and x is the ACT score. The researchers collected data from 60 freshmen who had taken both exams. Use the attached dataset to estimate the above regression equation in Excel. Use the regression results to answer the following 10 questions (1)-(10). The data "Scores" is attached. Scores.xlsx What is the independent variable and what is the dependent variable in this research? (2 points) Based on the regression results, estimate the slope b and the y-intercept a in the regression equation y = a + bx. (2 points) Find the correlation coefficient r between x and y. (2 points) Report the coefficient for x (the slope) with its standard error. (2 points) Construct the test for the hypothesis H0: b = 0. Give the t-stat and p-value. (2 points) Is the coefficient for ACT significant at α = 0.10 significant level? (2 points) Can you reject the null hypothesis H0: b = 0? (2 points) Interpret the meaning of the coefficient. Is the ACT score a strong influence on the SAT score? (2 points) Identify R2 from the regression results. Explain the meaning of R2. (2 points) Sandy is a freshman who took the ACT exam. Her score was 23. How do you predict her SAT score based on the regression result? (2 points)
Dominador T.
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