Data were collected from a sample of World Campus STAT 200 students during the S
ID: 2909025 • Letter: D
Question
Data were collected from a sample of World Campus STAT 200 students during the Spring 2018 semester. The instructor wants to know if there is evidence of a relationship between students’ scores on the midterm practice quiz and the midterm exam in the population of all World Campus STAT 200 students. All assumptions were met for using linear regression techniques. The following output was obtained from Minitab Express for a simple linear regression model using midterm practice quiz scores to predict midterm exam scores.
E. If a student has a midterm practice quiz score of 14, what is this student’s predicted midterm exam score?
F. A student has a midterm practice quiz score of 14 and a midterm exam score of 55. Compute this student’s residual.
G. Interpret the residual that you computed in part F.
H. Is it valid to use this regression model to predict the midterm exam scores of students in STAT 200 at Penn State York this semester? Explain why or why not.
Fitted Line Plot for Linear Model 50 45 40 35 30 10 12 13 14 15 Midterm Practice Quiz Analysis of Variance Source Regression 1 1230.91 1230.91 41.37Explanation / Answer
Answer
we have the regression equation, Midterm Exam = 19.765 + 2.2904*Midterm practice quiz
(E) when the midterm practice quiz = 14
we have Midterm Exam = 19.765 + 2.2904*14 = 9.765+32.0656 = 51.8306
so, the student's predicted midterm exam score is 51.8306
(F) First, we need to find the predicted midterm exam score using the given value of midterm practice quiz score = 14
using the regression equation, we get Midterm Exam = 19.765 + 2.2904*Midterm practice quiz
setting the value of midterm practice quiz score = 14
we get
Midterm Exam = 19.765 + 2.2904*55 = 19.765 + 32.0656 =81.8306
So, Residual = difference between actual and predicted score= 55-51.8306 = 3.1694
(G) The residual computed in part F is the difference between the actual and predicted midterm exam score for a student who has scored 14 points in the midterm practice quiz. The calculated value is less than actual value which means that there are some factors which affected the midterm exam score.
(H) Yes, it is valid to use this regression model because we can see that the p value corresponding to the constant and independent variable midterm practice quiz are significant and the p value for the F test is also significant. Thus, we can use this regression model to predict the midterm exam scores of students in the STAT 200 as Penn State York this semester
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