2. Data were collected from a sample of World Campus STAT 200 students during th
ID: 2908983 • Letter: 2
Question
2. 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. (40 points)
A. In this model, what is the explanatory variable and what is the response variable? Explain how you determined this.
B. Identify and interpret the coefficient of determination.
C. Using this output, determine the correlation (Pearson’s r) between midterm practice quiz scores and midterm exam scores.
D. Are midterm practice quiz scores a statistically significant predictor of midterm exam scores? Explain how you determined this.
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 Miderm Practice Analysis of Variance Source DF Adj SS Regression 123091 12301 437 0.0001 Error Tota 90 2678.08 29.76 1 3908.99 Model Summary 5.45495 31.49% 30.73% Coefficients Tenm Constant Midterm Practice Quiz 2.2904 0.3581 643 .0001 Coef SE Coef T-Value P-Value 19.765 4.820 4.10 0.0001 Regression Equation Midterm Exam-19.765+2.2904 Midterm Practice QuizExplanation / Answer
A.Midterm Exam Score is the response variable and Midterm Practice Quiz Score is the explanatory variable, which can be well understood from the Regression Equation since Midterm Exam Score is on the LHS and Midterm Practice Quiz Score is on the RHS of the eqn.
B. Coefficient of determination : R-sq = 31.49% means that 31.49% of the total variation is explained by the regression equation.
C. Pearson’s correlation r = ?R-sq = ?0.3149 = 0.5611595.
D. Yes, Midterm Practice Quiz score is significant in the regression equation since the p-value <0.0001 (<< 0.05, i.e << significance level ) is given in the coefficient output.
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