The director of admissions at a small college selected 120 students at random fr
ID: 3274098 • Letter: T
Question
The director of admissions at a small college selected 120 students at random from the new freshman class in a study to determine whether a students grade point average (GPA) at the end of the freshman year can be predicted from their ACT test score. (The data is below)
1- Find the parameters of the regression line
2 - Would it be more resonable to consider X as known constants or as random variable
3- If X were considered to be random variables. Would that have any effect on prediction intervals for new applicants. Explain
Explanation / Answer
following information has been generated using given data
(a) the regression line y=a+bx or GPA=a+b*ACT is givne as
GPA=2.11405+0.03883ACT
(b) X is not random variable, no assumptions of any predictor (i.e. independent) variables.
(c)Regression is inherently a model about the outcome variable. What predicts its value and how well? The nature of how predictors relate to it (linearly, quadratically, multiplicatively?). How much of its variance can be explained by the predictors, and how much is just random? The focus is all on that outcome.
Analysis of Variance Source DF Sum of Mean F Value P-value Squares Square Model 1 3.58785 3.58785 9.24 0.0029 Error 118 45.81761 0.38828 Corrected Total 119 49.40545 Root MSE 0.62313 R-Square 0.0726 Dependent Mean 3.07405 Adj R-Sq 0.0648 Coeff Var 20.27049 Parameter Estimates Variable DF Parameter Standard t Value P-value Estimate Error Intercept 1 2.11405 0.32089 6.59 <.0001 ACT 1 0.03883 0.01277 3.04 0.0029