Business Statistics Homework: Descriptive Stats, Regression Analysis

This assignment solution delves into the realm of business statistics, providing a comprehensive analysis of a dataset. It begins by calculating and interpreting descriptive statistics for various variables, including central tendency, variability, and shape, for student marks, raised hands, and grade IDs. The solution also addresses the interpretation of dummy variables like gender and subject, providing insights into their significance. Furthermore, it includes graphical representations of data distributions, such as histograms and box-and-whisker plots, along with interpretations of normality and the presence of outliers. The assignment extends to hypothesis testing, specifically examining a school administrator's claim regarding student performance in a religion course. The solution also incorporates multiple linear regression, covering coefficient estimates, interpretation of slope coefficients, R-squared values, and the statistical significance of the model. The assignment concludes with a prediction of student marks under specific conditions and an assessment of whether the regression model satisfies the assumptions of linearity, normality, and homoscedasticity, along with a discussion of the data's representativeness of the population and suggestions for improved sampling procedures.

Business statistics

TABLE OF CONTENTS
Question 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, raisedhands and GradeID.
How would you interpret the mean of dummy variables such as Female or Math?...................3
Draw a graph that displays the distribution of Student Marks. Be sure to comment on the
distribution. Does it appear normally distributed?....................................................................10
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....................................10
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.........................................................................................23
(G) Multiple linear regression...................................................................................................24
(H) Coefficient estimate for raised hands..................................................................................25
(I)Interpretation of slope coefficients........................................................................................25
(J) R square and adjusted R square............................................................................................26
(K) Statistical significance of model.........................................................................................26
(L) Variables that can be taken in to consideration...................................................................26
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.................................................................26
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...........................................................27
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.........................................................................................................................................28

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?......................................................................28

Question 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, raisedhands and GradeID.
How would you interpret the mean of dummy variables such as Female or Math?
Marks
Mean 76.73333
Standard
Error 0.800807
Median 80
Mode 92
Standard
Deviation 17.5448
Sample
Variance 307.8202
Kurtosis -0.52198
Skewness -0.70473
Range 65
Minimum 35
Maximum 100
Sum 36832
Count 480
Largest(1) 100
Smallest(1) 35
Confidence
Level(95.0%) 1.573529
Above mentioned results of the central tendency about the marks obtained by all the
student shows that majority of students has gain marks in the range of 76 which is regarded as
the distinction marks. The minimum marks gained by students is 80 and mode of the students has
gained 92 that shows the ability of all the students due to the impact of course enrolled by
students.
Grade Id
Mean 5.6
Standard
Error 0.129657
Median 7
Mode 2
Standard 2.840653

Deviation
Sample
Variance 8.069311
Kurtosis -1.04107
Skewness 0.026977
Range 10
Minimum 2
Maximum 12
Sum 2688
Count 480
Largest(1) 12
Smallest(1) 2
Confidence
Level(95.0%) 0.254768
Grade Id of all the students shows stable position in relation to the various measures of
central tendency that includes both mean, median and mode. The changes incurred in the grade
Id is less as compared to the mean of all grade of the students.
Raised hand
Mean 46.775
Standard
Error 1.404873
Median 50
Mode 10
Standard
Deviation 30.77922
Sample
Variance 947.3605
Kurtosis -1.497
Skewness 0.026962
Range 100
Minimum 0
Maximum 100
Sum 22452
Count 480
Largest(1) 100
Smallest(1) 0
Confidence
Level(95.0%) 2.760475

Most of the students in college raises their hand as this shows the interest of all the
students towards he course they enrolled to as majority of students whether male of female raised
their hands in the class.
Visited
resources
Mean 54.79792
Standard
Error 1.509889
Median 65
Mode 80
Standard
Deviation 33.08001
Sample
Variance 1094.287
Kurtosis -1.4852
Skewness -0.34244
Range 99
Minimum 0
Maximum 99
Sum 26303
Count 480
Largest(1) 99
Smallest(1) 0
Confidence
Level(95.0%) 2.966824
AnnouncementsView
Mean 37.91875
Standard Error 1.214632
Median 33
Mode 12
Standard Deviation 26.61124
Sample Variance 708.1583
Kurtosis -1.00224
Skewness 0.399243
Range 98
Minimum 0
Maximum 98
Sum 18201
Count 480

Largest(1) 98
Smallest(1) 0
Confidence
Level(95.0%) 2.386665
Discussion
Mean 43.28333
Standard
Error 1.261484
Median 39
Mode 70
Standard
Deviation 27.63774
Sample
Variance 763.8444
Kurtosis -1.12656
Skewness 0.362594
Range 98
Minimum 1
Maximum 99
Sum 20776
Count 480
Largest(1) 99
Smallest(1) 1
Confidence
Level(95.0%) 2.478727
Maths
Mean 0.241667
Standard
Error 0.01956
Median 0
Mode 0
Standard 0.42854
Female
Mean 0.364583
Standard
Error 0.021992
Median 0
Mode 0
Standard
Deviation 0.481815
Sample
Variance 0.232146
Kurtosis -1.68843
Skewness 0.564462
Range 1
Minimum 0
Maximum 1
Sum 175
Count 480
Largest(1) 1
Smallest(1) 0
Confidence
Level(95.0%) 0.043212

Deviation
Sample
Variance 0.183646
Kurtosis -0.53649
Skewness 1.210689
Range 1
Minimum 0
Maximum 1
Sum 116
Count 480
Largest(1) 1
Smallest(1) 0
Confidence
Level(95.0%) 0.038434
It can be revealed from the above results of the descriptive statistics that mean of math is less as
compared to the female that shows that majority of female members as compared to the singular
subjects out of all other subjects.
Science
Mean 0.26875
Standard
Error 0.020255
Median 0
Mode 0
Standard
Deviation 0.443772
Sample
Variance 0.196934
Kurtosis -0.90851
Skewness 1.046562
Range 1
Minimum 0
Maximum 1
Sum 129
Count 480
Largest(1) 1
Smallest(1) 0
Confidence
Level(95.0%) 0.0398
Language

Mean 0.404167
Standard
Error 0.022422
Median 0
Mode 0
Standard
Deviation 0.491242
Sample
Variance 0.241319
Kurtosis -1.85424
Skewness 0.3918
Range 1
Minimum 0
Maximum 1
Sum 194
Count 480
Largest(1) 1
Smallest(1) 0
Confidence
Level(95.0%) 0.044058
Religion
Mean 0.045833
Standard
Error 0.009555
Median 0
Mode 0
Standard
Deviation 0.209342
Sample
Variance 0.043824
Kurtosis 17.05584
Skewness 4.357154
Range 1
Minimum 0
Maximum 1
Sum 22
Count 480
Largest(1) 1
Smallest(1) 0
Confidence
Level(95.0%) 0.018775

History
Mean 0.039583
Standard
Error 0.008909
Median 0
Mode 0
Standard
Deviation 0.195182
Sample
Variance 0.038096
Kurtosis 20.53008
Skewness 4.737568
Range 1
Minimum 0
Maximum 1
Sum 19
Count 480
Largest(1) 1
Smallest(1) 0
Confidence
Level(95.0%) 0.017505

Draw a graph that displays the distribution of Student Marks. Be sure to comment on the
distribution. Does it appear normally distributed?
Above histogram shows the increasing trend butal the data is not propery distrbued using normal
disribution of data due to which various variatons incured in the above set of data.
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.
Difference
Raised
hands Mean 46.775
Min 0 STDV 30.77922
q1-min 15.75
median-q1 34.25
q3-median 25
max-q3 25

Raised hands Z Outlier=Z>3
15 -1.03235 FALSE
20 -0.86991 FALSE
10 -1.1948 FALSE
30 -0.54501 FALSE
40 -0.22012 FALSE
42 -0.15514 FALSE
35 -0.38256 FALSE
50 0.104778 FALSE
12 -1.12982 FALSE
70 0.754567 FALSE
50 0.104778 FALSE
19 -0.90239 FALSE
5 -1.35725 FALSE
20 -0.86991 FALSE
62 0.494652 FALSE
30 -0.54501 FALSE
36 -0.35007 FALSE
55 0.267226 FALSE
69 0.722078 FALSE
70 0.754567 FALSE
60 0.429673 FALSE
10 -1.1948 FALSE
15 -1.03235 FALSE
2 -1.45472 FALSE
0 -1.51969 FALSE
8 -1.25978 FALSE
19 -0.90239 FALSE