Data were collected from a sample of World Campus STAT 200 students during the S

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.

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.

Explanation / Answer

Part A

In the given regression model, the explanatory or independent variable is given as midterm practice quiz and the response or dependent variable is given as midterm exam, because we predict the midterm exam scores based on the midterm practice quiz. Also, the variable midterm practice quiz is given in the regression coefficients list in the regression output. Also, regression equation is given at the end of regression output and it indicate that the variable midterm practice quiz is independent or explanatory variable and midterm exam is dependent or response variable.

Part B

Coefficient of determination or the value of R square for this regression model is given as 0.3149, this means about 31.49% of the variation in the dependent variable midterm exam is explained by the independent variable midterm practice quiz.

Part C

Pearson’s correlation coefficient = r = sqrt(R square) = sqrt(0.3149) = 0.56116

The correlation coefficient between midterm practice quiz scores and midterm exam scores is given as r = 0.56116. There is a considerable positive association exists between given two variables.

Part D

Midterm practice quiz scores is a statistically significant predictor of midterm exam scores, because the p-value for this regression model is given as 0.0001 which is less than 5% level of significance or alpha value 0.05.

Part E

We are given

Midterm exam score = 19.765 + 2.2904*Midterm Practice Quiz

Midterm Practice Quiz score = 14

Midterm exam score = 19.765 + 2.2904*14

Midterm exam score = 51.8306

Part F

Residual = Observed value – predicted value

We are given

Observed value of midterm exam score when midterm practice quiz is 14 = 55

Predicted value of midterm exam score when midterm practice quiz is 14 = 51.8306

Residual = 55 - 51.8306

Residual = 3.1694

Part G

There is a 3.17 points distance exist between the predicted score and actual score when midterm practice quiz score is 14.

Part H

It is not valid to use this regression model to predict the midterm exam scores of students in STAT 200 at Penn State York this semester, because given regression model is constructed for the population of World Campus STAT 200 students.

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