BUSINESS STATISTICS PROJECT

Problem Description:

A regional school in Victoria has asked us to evaluate the role of their learning management system in assisting students. We have collected data on 480 students between Year 2 and Year 12.

You will use descriptive statistics, inferential statistics and your knowledge of multiple linear regression to complete this task.

Mark (Dependent Variable) and several characteristics (Independent Variables) are given in the Excel file: WedThuFri.xlsx.  You can find the data that we will use in the project in the "Processed" tab with the definitions of the variables in the "Dictionary" tab.

Required:

A. Calculate the descriptive statistics from the data and display in a table.  Be sure to comment on the central tendency, variability and shape for Mark, raised hands and GradeID. How would you interpret the mean of dummy variables such as Female or Math?

B. Draw a graph that displays the distribution of Student Marks.  Be sure to comment on the distribution. Does it appear normally distributed?

C. Create a box-and-whisker plot for the distribution of the times that students have raised their hands and describe the shape.  Is there evidence of outliers in the data?

D. What is the probability that we could randomly select a student whose mark is at least 70?  What is the likelihood that a student enrolled in maths has a mark at least 70? Is the mark statistically independent of whether they are enrolled in maths?  Use a Contingency Table.

E. Estimate the 95% confidence interval for the population mean times a female student raised hands.  How does this compare to the 95% confidence interval for the population mean times a male student raised hands?

F. A school administrator believes that students enrol in a religion course as they believe it is a "sluff" class, or a class that students can consistently obtain a mean of more than 70.Test his claim at the 5% level of significance.

G. Run a multiple linear regression using the data and show the output from Excel. Exclude the dummy variable History from the regression results.

H. Is the coefficient estimate for Raised Hands statistically different than zero at the 5% level of significance?  Set-up the correct hypothesis test using the results found in the table in Part (G) using both the critical value and p-value approach.  Interpret the coefficient estimate of the slope.

I. Interpret the remaining slope coefficient estimates. Discuss whether the signs are what you are expecting and explain your reasoning.

J. Interpret the value of the Adjusted R2.Is there a large difference between the R2 and the Adjusted R2? If so, what may explain the reasoning for this?

K. Is the overall model statistically significant at the 5% level of significance?  Use the p-value approach.

L. Based on the results of the regressions, what other factors would have influenced marks?  Provide a couple possible examples and indicate their predicted relationship with sales if they were included.

M. Predict the average marks of a student in Year 6 who has raised their hand 35 times, visited 40 resources, looked at 75 announcements, participated in 5 discussions, is a Female in a Math course. Discuss if it is appropriate to predict the marks of students under these conditions.  Show the predicted regression equation.

N. Do the results suggest that the data satisfy the assumptions of a linear regression: Linearity, Normality of the Errors, and Homoscedasticity of Errors?  Show using scatter diagrams, normal probability plots and/or histograms and Explain.

O. Does this data provide information on the true population distribution of students in Victoria? Explain and if not, describe a sampling procedure that could lead to more accurate results.

P. The school is looking to promote higher enrolment of girls into mathematic courses and is looking to interview five girls enrolled in a maths course. What is the likelihood that if they would select none who had a mark at least a 90?  What is the likelihood that all five would have a mark at least 90?  How do these compare for men?  Explain your results and show a binomial table. (Note: Please ignore that we are technically violating rules of binomial experiments).

Attachment:- Assignment Files.rar