Comparison & Regression Questions Use the following scenario to answer questions
ID: 3361804 • Letter: C
Question
Comparison & Regression Questions
Use the following scenario to answer questions 1 and 2.
A university is interested in the holistic wellness of students attending the institution. Given extensive wellness programming that occurs each year, the university believes students’ wellness improves each year they are enrolled. In order to determine if this is true, the university took a wellness measurement on students (wellness score) and compared by classification (freshman, sophomore, junior, senior) to determine if there are differences. The resulting 1 X 4 ANOVA resulted in a rejection of the HO. As such, the university must now determine where the differences occurred.
List the HO for each pairwise post hoc comparison.
How will you know from the pairwise post hoc comparisons where the difference(s) in the levels occur?
When would you perform a priori planned comparisons instead of pairwise omnibus post hoc comparisons?
What advantage does a priori planned comparisons have over pairwise omnibus post hoc comparisons?
Use the following scenario to answer questions 5 –8
A university admissions officer wants to impress his/her supervisor with newly acquired statistical knowledge. The admissions officer believes he/she can use high school GPA, high school class rank, SAT score, and ACT score to predict the first semester GPA of entering freshman students. The admissions officer decides to utilize multiple regression.
What is the criterion variable?
What are the predictor variables?
What is the unstandardized regression equation?
If the resulting analysis yields a coefficient of determination of r2=.47, what do we know?
Explanation / Answer
Criterion varible: Criterion variable is the variable which is to be predicted or the dependent varibale. In this case the criterion variable is the first semister GPA of entering freshman students.
Predictor Variable: Predictor variable is the variable which is used to predict another variable. This is also called the independent variable. In this case high school GPA, high school class rank, SAT score, and ACT score are all predictor variables.
Unstandardized regression equation: If an independent variable is expressed in millions or billions of units(for eg, 656,765), it can have unstandardized estimate close to zero. To make the coefficient value more interpretable, we can rescale the variable by dividing the variable by 1000 or 100,000 (depending on the value). After rescaling the variable, run regression analysis again including the transformed variable. You would find beta coefficient larger than the old coefficient value and significantly larger than 0.
The coefficient of determination (denoted by R2) is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.
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