Problem 4: Variables that may affect Grades The data set contains a random sample of STAT 250 Final Exam Scores out of 80 points. For each individual sampled, the time (in hours per week) that the stu...

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Problem 4: Variables that may affect Grades The data set contains a random sample of STAT 250 Final Exam Scores out of 80 points. For each individual sampled, the time (in hours per week) that the stu...

Problem 4: Variables that may affect Grades The data set contains a random sample of STAT 250 Final Exam Scores out of 80 points. For each individual sampled, the time (in hours per week) that the student spent participating in a GMU club or sport and working for pay outside of GMU was recorded. Values of 0 indicate the students either does not participate in a club or sport or does not work a job for pay. The goal of this problem is to explore the two time variables and see how each affects their Final Exam Score. The Final Exam Score variable is the response variable in this problem.
a) Investigate the relationship between the explanatory variable “Club or Sport Time” and response variable “Final Exam Score” by doing the following: i) Make a properly titled and labeled scatterplot and copy and paste it in your solutions (use Graph  Scatter Plot in StatCrunch). ii) Calculate the correlation coefficient (use Stat  Summary Stats  Correlation in StatCrunch). Provide this value in your document. iii) Interpret the scatterplot and correlation coefficient in terms of trend, strength, and shape (form) in one complete sentence.
b) Investigate the relationship between the explanatory variable “Paid Job Time” and response variable “Final Exam Score” by doing the following: i) Make a properly titled and labeled scatterplot and copy and paste it in your solutions (use Graph  Scatter Plot in StatCrunch). ii) Calculate the correlation coefficient (use Stat  Summary Stats  Correlation in StatCrunch). Provide this value in your document. iii) Interpret the scatterplot and correlation coefficient in terms of trend, strength, and shape (form) in one complete sentence.

c) Which variable do you believe has the most effect on the Final Exam Score? Compare the two above R2 values to make your decision.

d) Using the variable with the highest R2 value as the explanatory variable, run a Simple Linear Regression analysis in StatCrunch. Use Stat  Regression  Simple Linear. Copy and paste only the StatCrunch results output (no tables).

e) Add the fitted line plot to your document. This graph appears on page 2 of your output.

f) Type the regression equation into your document.

g) Interpret the slope of the regression line (in context of this data set).

h) Is it meaningful to interpret the y-intercept? Why or why not?

i) State R2 (r-squared) (i.e., the coefficient of determination) and explain what this value means in context of the data set.

j) Use the regression equation from part (d) to predict the Final Exam Score for an individual who works 30 hours a week. State your predicted value in a sentence that is in context of the data. Note: You can do this calculation “by hand” or using StatCrunch.

k) Is your prediction in part (h) an example of extrapolation? Why or why not?

Data set: Exam Scores.

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math Statistics-And-Probability

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Answer 1

Answer #1

SOLUTION

a) iii) Relationship between Club or Sport time and Final exam score:

From the scatterplot, the following points can be observed:

Trend: There is a slightly decreasing trend
Strength: The strength of the correlation is really less
Shape: There is a cluster for small values of Club or Sport time.

From the correlation coefficient, it can also be observed that there is a slight negative correlation between the two variables.

Interpretation: Though Club or Sport time has a slight negative impact on final exam score, it can be said that if club or sport time is less or moderate then final exam score is high but if club or sport time is high then due to insufficient datapoints we can't find out any relation.

b) iii) Relationship between Paid work time and Final exam score:

From the scatterplot, the following points can be observed:

Trend: There is a clear decreasing trend
Strength: The strength of the correlation is high as most of the data points fall on a straight line
Shape: The plot shows a linear pattern.

From the correlation coefficient, it can also be observed that there is a moderately high negative correlation between the two variables.

Interpretation: Paid work time has a moderately strong negative impact on final exam score with a high degree or strength of scattering and it follows a linear pattern.

c) R-sq(for paid work time)=0.55609

R-sq(for club or sport time)=0.06133

According to the R-sq value, paid work time has a greater influence on final exam score than club or sport time.

d),e) & f) These answers should relate to paid work time as the R-sq is higher for this variable.

g) The slope denotes the increase in final exam score for a unit increase in paid work time.

h) Yes, it is meaningful. Even if there is no paid work time the final exam score may not be zero as there are lots of other factors on which the final exam score depends.

i) The R-sq for paid work time is 0.55609, which implies that 55.609% of the total variation in final exam score can be explained by the regression equation of the final exam score on paid work time.

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Problem 4: Variables that may affect Grades The data set contains a random sample of STAT 250 Final Exam Scores out of 80 points. For each individual sampled, the time (in hours per week) that the stu...

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Problem 4: Variables that may affect Grades The data set contains a random sample of STAT 250 Final Exam Scores out of 80 points. For each individual sampled, the time (in hours per week) that the stu...

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Add Answer to: Problem 4: Variables that may affect Grades The data set contains a random sample of STAT 250 Final Exam Scores out of 80 points. For each individual sampled, the time (in hours per week) that the stu...

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Problem 4: Variables that may affect Grades The data set contains a random sample of STAT 250 Final Exam Scores out of 80 points. For each individual sampled, the time (in hours per week) that the stu...