## As shown in several lectures there are two distinct methods of calculating summary or descriptive statistics using Excel.

### statistics

##### Description

As an example for the regression results in question 5 you will need to present the results in traditional form e.g.

Final_exam = 2.05 + 1.8Tutorial_ attend

(1.7)    (0.45)

Figures in parentheses represent standard errors

No. of observations 737, Rsquared 0.29. (These results are illustrative only- i.e. I made them up.)

Then you would interpret and carry out relevant hypothesis tests.

Problem Description:

You have been appointed by the Dean of Business to analyse student performance in a course offered by a Business School. The focus is upon the key determinants of the Final_exam (i.e. the students’ final exam mark), in particular the role of the Assignment (i.e. Assignment_grade) and Tutorial_attend (i.e. the number of tutorials attended during the semester). Using the tools learned in your current Business Statistics course provide the Dean with an analysis of Final_exam performance.

1.      As shown in several lectures there are two distinct methods of calculating summary or descriptive statistics using Excel. This question requires you to use both methods. First use Excel Data Analysis Tool Pack (the descriptive statistics option) to calculate summary statistics for all variables included in the attached data file. Comment on your summary statistics including any differences across the 3 included variables, i.e. Final_exam, Assignment_mark and Tutorial_attend.  Carefully interpret. Second use excel to calculate all descriptive statistics documented in your report. These calculations should be carefully laid out in excel and should use excel formula NOT Data Analysis Toolpack. [Topic 1]

2.      Use appropriate graphs to interpret the relationship between (i) Final_exam and assignment_grade; (ii) Final_exam and Tutorial_attend; and (iii) assignment_grade and Tutorial_ attend. Carefully interpret and explain. [Topics 1]

3.      Calculate the sample correlation and covariance for the above 3 relationships in question 2. Carefully interpret your results. Once again use Excel for these calculations using both methods i.e. Data Analysis Tool Pack (options covariance, correlation) and using Excel formulae without use of Data Analysis Tool Pack. (Hint- if you find a discrepancy in your answers between the 2 excel methods can you explain why?)

4.      For this question ONLY, assume that the first 26 observations are male (i.e. rows 2-27 of the original data) and the last 29 observations are female. Use Excel both with and without Data Analysis Tool Pack to test the null hypothesis that the mean of the Final_exam is equal for males and females. Interpret your results. [Topics 6-8].  Do not include analysis by gender in any further parts of the analysis i.e. questions 5, 6 and 7.

5.      Use simple regression to explore the relationship between (i) Final_exam (Y) and assignment_grade (X); (ii) Final_exam (Y) and Tutorial_attend (X). Carry out any relevant hypothesis tests using a two-tailed hypothesis test approach at the 5% significance level. You may use Data Analysis Tool Pack for this. Carefully interpret and explain.  [Topics 9-10]

6.      Now use multiple regression to explore the relationship between Final_exam (Y), assignment_grade (X1) and Tutorial_attend (X2). You may use Data Analysis Tool Pack for this. Carry out any relevant two-tailed hypothesis tests at the 5% significance level. Carefully interpret. If you had a magic wand and could request additional data for your analysis of this course, what extra variables would you request and why? [Topic 10-11]

7.      Using your multiple regression results to predict Final_exam for a student with the mean assignment_grade and tutorial_attend equal to (i) 2 tutorials, (ii) 3, (iii) 4 and (iv) 5 tutorials. (Hint this means you will have 4 distinct predictions for Final_exam) Carefully interpret your results.