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BSB123-Data Analysis

Question

Answered

Task

A researcher is interested in the factors that may explain the academic achievement of first year Business students. With the university’s support, the researcher developed a standardised test that was to be undertaken by a random sample of students. The test contained questions related to the core business units of accountancy, marketing, management and statistics, and was administered towards the end of the each students first year of study. In addition to answering the test, the students were asked questions on their gender, age, mother’s highest level of education, whether the student was currently in a ‘romantic’ relationship. Students were also asked to report the number of instances where they did not attend either a lecture or a tutorial. In total, 649 students sat the test and a portion of the dataset1,2 is presented below:

Task 1 (Histogram, Boxplot and t-tests) 

(a) Construct a histogram of student results and briefly comment on its shape (central location and skewness). (2 marks)

(b) Construct a side-by-side boxplot of Result for male and female science students, and compare their distributions (central location, spread and skewness). (2 marks)

(c) Test if there is any difference in Results on average between male and female students at the 5% level of significance.

2. One would expect that students that have higher lecture absences or those involved in a romantic relationship may not perform as well as their peers,

(a) Test at the level of significance of 5% if students who missed 4 or more classes have a lower result than the students who missed three of less classes. (2 marks)

(b) Test at the level of significance of 5% if students who are involved in a romantic relationship have a lower result than the students who are not.

Task 2 (Regression Analysis)

You plan to develop a regression model to further investigate how various factors influence students’ Result. 

3. Before you conduct any regression analysis, you use Excel to construct a correlation matrix of all the quantitative variables in the dataset. Based on the correlation matrix, comment on the linear associations between Result and other quantitative variables (viz. Age, Medu, Lectures and Tutorials) and whether these variables could be used as a predictor of result. 

4. Based on the correlation matrix obtained in Question 3, would you say that:

(i) Age is a predictor of Result?

(ii) MEdu is a predictor of Result?

(iii) Lectures is a predictor of Result?

(iv) Tutorials is a predictor of Result? Conduct simple regression to support your answers to questions (i) to (iv)

5. You conduct a stepwise regression according to the following procedure:

Step 1: Gender only

Step 2: Gender and Age

Step 3: Gender, Age and Medu

Step 4: Gender, Age, Medu and Relationship

Step 5: Gender, Age, Medu, Relationship and Lectures Step 6: Gender, Age, Medu, Relationship, Lectures and Tutorials Present the regression output for each of the six steps. 

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