Data were collected from a sample of World Campus STAT200 students from the Summ
ID: 3312702 • Letter: D
Question
Data were collected from a sample of World Campus STAT200 students from the Summer 2017 semester. We want to know if there is a relationship between students' Wiley PLUS scores (out of 100 points) and scores on the midterm exam (out of 50 points) in the population of all World Campus STAT200 students. All assumptions were checked and were met for using linear regression techniques. The following output was obtained from Minitab Express for a simple linear regression model using Wiley PLUS scores to predict midterm exam scores. Analysis of Variance Source Regression 162.246 162246 9.17 0.0050 Error Total DF MS F-Value P-Value 30 530.834 17.694 31 693.079 Model Summary 4.20648 23.41% 20.86% Coefficients Term Constant 34.996 3.246 0.780.0001 WleyPLUS 0.10968 0.03622 3.03 0.0050 Coef SE Coef T-Value P-Value Regression Equation Midterm Exam 34.996+0.10968 WileyPLUS a. Write the regression equation from the output above. b. If a student has a Wiley PLUS score of 85, what is this student's predicted midterm exam score? Be sure to show all work for credit! c. A student has a Wiley PLUS score of 100 and a midterm score of 47. Compute this student's residual. Show all work for credit! Interpret the student's residual that you computed in part c. Identify and interpret the coefficient of determination. d. e.Explanation / Answer
a) Regression equation is
Midterm Exam=34.996+0.10968 wileyplus.
b) wileyPlus=85 then
Midterm Exam=34.996+0.10968 *85
c) we are given y=100 and x=47
Midterm Exam=34.996+0.10968 *47=40.15
Residul=value -predicted value =100-40.15=59.84
d) interpriration of residual
the predicted value is far from the original value.
e) R-sq is called the coefficient of determination
R-sq=23.41
Interpretation : 23.41 variation is explained by the Wiley Plus
f) r=sqrt(R-sq) =sqrt(0.2341)= 0.48
g) it is ibvalid model, there is very low R-square value
thanks
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