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 gr...Read More

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

25 -0.70746 FALSE
75 0.917015 FALSE
30 -0.54501 FALSE
35 -0.38256 FALSE
4 -1.38974 FALSE
2 -1.45472 FALSE
8 -1.25978 FALSE
12 -1.12982 FALSE
10 -1.1948 FALSE
8 -1.25978 FALSE
45 -0.05767 FALSE
0 -1.51969 FALSE
50 0.104778 FALSE
14 -1.06484 FALSE
19 -0.90239 FALSE
10 -1.1948 FALSE
30 -0.54501 FALSE
33 -0.44754 FALSE
20 -0.86991 FALSE
7 -1.29227 FALSE
70 0.754567 FALSE
13 -1.09733 FALSE
29 -0.5775 FALSE
20 -0.86991 FALSE
39 -0.25261 FALSE
55 0.267226 FALSE
49 0.072289 FALSE
12 -1.12982 FALSE
16 -0.99986 FALSE
19 -0.90239 FALSE
5 -1.35725 FALSE
28 -0.60999 FALSE
27 -0.64248 FALSE
21 -0.83742 FALSE
50 0.104778 FALSE
80 1.079462 FALSE
17 -0.96737 FALSE
0 -1.51969 FALSE
13 -1.09733 FALSE
25 -0.70746 FALSE
65 0.59212 FALSE
70 0.754567 FALSE
39 -0.25261 FALSE

22 -0.80493 FALSE
29 -0.5775 FALSE
11 -1.16231 FALSE
19 -0.90239 FALSE
12 -1.12982 FALSE
50 0.104778 FALSE
15 -1.03235 FALSE
20 -0.86991 FALSE
13 -1.09733 FALSE
80 1.079462 FALSE
8 -1.25978 FALSE
8 -1.25978 FALSE
7 -1.29227 FALSE
7 -1.29227 FALSE
50 0.104778 FALSE
1 -1.4872 FALSE
70 0.754567 FALSE
19 -0.90239 FALSE
3 -1.42223 FALSE
5 -1.35725 FALSE
4 -1.38974 FALSE
80 1.079462 FALSE
50 0.104778 FALSE
55 0.267226 FALSE
80 1.079462 FALSE
100 1.729251 FALSE
14 -1.06484 FALSE
6 -1.32476 FALSE
10 -1.1948 FALSE
50 0.104778 FALSE
50 0.104778 FALSE
70 0.754567 FALSE
2 -1.45472 FALSE
1 -1.4872 FALSE
0 -1.51969 FALSE
0 -1.51969 FALSE
12 -1.12982 FALSE
70 0.754567 FALSE
7 -1.29227 FALSE
90 1.404356 FALSE
70 0.754567 FALSE
77 0.981994 FALSE
2 -1.45472 FALSE

25 -0.70746 FALSE
11 -1.16231 FALSE
0 -1.51969 FALSE
77 0.981994 FALSE
25 -0.70746 FALSE
24 -0.73995 FALSE
60 0.429673 FALSE
21 -0.83742 FALSE
0 -1.51969 FALSE
66 0.62461 FALSE
70 0.754567 FALSE
0 -1.51969 FALSE
12 -1.12982 FALSE
2 -1.45472 FALSE
55 0.267226 FALSE
12 -1.12982 FALSE
70 0.754567 FALSE
7 -1.29227 FALSE
80 1.079462 FALSE
0 -1.51969 FALSE
12 -1.12982 FALSE
80 1.079462 FALSE
70 0.754567 FALSE
70 0.754567 FALSE
60 0.429673 FALSE
100 1.729251 FALSE
100 1.729251 FALSE
10 -1.1948 FALSE
19 -0.90239 FALSE
10 -1.1948 FALSE
80 1.079462 FALSE
10 -1.1948 FALSE
70 0.754567 FALSE
100 1.729251 FALSE
10 -1.1948 FALSE
60 0.429673 FALSE
100 1.729251 FALSE
80 1.079462 FALSE
23 -0.77244 FALSE
100 1.729251 FALSE
10 -1.1948 FALSE
70 0.754567 FALSE
70 0.754567 FALSE

70 0.754567 FALSE
70 0.754567 FALSE
22 -0.80493 FALSE
62 0.494652 FALSE
82 1.144441 FALSE
72 0.819546 FALSE
70 0.754567 FALSE
60 0.429673 FALSE
55 0.267226 FALSE
72 0.819546 FALSE
51 0.137268 FALSE
80 1.079462 FALSE
60 0.429673 FALSE
30 -0.54501 FALSE
40 -0.22012 FALSE
60 0.429673 FALSE
20 -0.86991 FALSE
20 -0.86991 FALSE
50 0.104778 FALSE
10 -1.1948 FALSE
60 0.429673 FALSE
15 -1.03235 FALSE
80 1.079462 FALSE
40 -0.22012 FALSE
60 0.429673 FALSE
50 0.104778 FALSE
85 1.241909 FALSE
25 -0.70746 FALSE
10 -1.1948 FALSE
87 1.306888 FALSE
85 1.241909 FALSE
80 1.079462 FALSE
75 0.917015 FALSE
85 1.241909 FALSE
23 -0.77244 FALSE
15 -1.03235 FALSE
95 1.566804 FALSE
81 1.111951 FALSE
53 0.202247 FALSE
15 -1.03235 FALSE
92 1.469335 FALSE
83 1.17693 FALSE
27 -0.64248 FALSE

45 -0.05767 FALSE
15 -1.03235 FALSE
45 -0.05767 FALSE
25 -0.70746 FALSE
22 -0.80493 FALSE
29 -0.5775 FALSE
72 0.819546 FALSE
67 0.657099 FALSE
17 -0.96737 FALSE
27 -0.64248 FALSE
70 0.754567 FALSE
27 -0.64248 FALSE
17 -0.96737 FALSE
87 1.306888 FALSE
7 -1.29227 FALSE
17 -0.96737 FALSE
5 -1.35725 FALSE
27 -0.64248 FALSE
87 1.306888 FALSE
96 1.599293 FALSE
57 0.332205 FALSE
77 0.981994 FALSE
80 1.079462 FALSE
62 0.494652 FALSE
72 0.819546 FALSE
87 1.306888 FALSE
72 0.819546 FALSE
2 -1.45472 FALSE
5 -1.35725 FALSE
73 0.852036 FALSE
5 -1.35725 FALSE
51 0.137268 FALSE
9 -1.22729 FALSE
19 -0.90239 FALSE
32 -0.48003 FALSE
32 -0.48003 FALSE
12 -1.12982 FALSE
52 0.169757 FALSE
72 0.819546 FALSE
72 0.819546 FALSE
92 1.469335 FALSE
72 0.819546 FALSE
72 0.819546 FALSE

22 -0.80493 FALSE
12 -1.12982 FALSE
70 0.754567 FALSE
50 0.104778 FALSE
80 1.079462 FALSE
87 1.306888 FALSE
70 0.754567 FALSE
65 0.59212 FALSE
15 -1.03235 FALSE
19 -0.90239 FALSE
69 0.722078 FALSE
39 -0.25261 FALSE
59 0.397184 FALSE
10 -1.1948 FALSE
80 1.079462 FALSE
70 0.754567 FALSE
80 1.079462 FALSE
69 0.722078 FALSE
10 -1.1948 FALSE
61 0.462162 FALSE
21 -0.83742 FALSE
49 0.072289 FALSE
70 0.754567 FALSE
79 1.046973 FALSE
19 -0.90239 FALSE
11 -1.16231 FALSE
10 -1.1948 FALSE
18 -0.93488 FALSE
90 1.404356 FALSE
92 1.469335 FALSE
42 -0.15514 FALSE
22 -0.80493 FALSE
95 1.566804 FALSE
90 1.404356 FALSE
72 0.819546 FALSE
92 1.469335 FALSE
82 1.144441 FALSE
72 0.819546 FALSE
74 0.884525 FALSE
74 0.884525 FALSE
95 1.566804 FALSE
97 1.631783 FALSE
40 -0.22012 FALSE

41 -0.18763 FALSE
51 0.137268 FALSE
81 1.111951 FALSE
71 0.787057 FALSE
75 0.917015 FALSE
49 0.072289 FALSE
42 -0.15514 FALSE
90 1.404356 FALSE
62 0.494652 FALSE
90 1.404356 FALSE
62 0.494652 FALSE
98 1.664272 FALSE
72 0.819546 FALSE
18 -0.93488 FALSE
32 -0.48003 FALSE
10 -1.1948 FALSE
22 -0.80493 FALSE
11 -1.16231 FALSE
12 -1.12982 FALSE
15 -1.03235 FALSE
32 -0.48003 FALSE
65 0.59212 FALSE
72 0.819546 FALSE
95 1.566804 FALSE
82 1.144441 FALSE
25 -0.70746 FALSE
42 -0.15514 FALSE
55 0.267226 FALSE
62 0.494652 FALSE
78 1.014483 FALSE
72 0.819546 FALSE
60 0.429673 FALSE
50 0.104778 FALSE
60 0.429673 FALSE
50 0.104778 FALSE
60 0.429673 FALSE
50 0.104778 FALSE
10 -1.1948 FALSE
30 -0.54501 FALSE
24 -0.73995 FALSE
27 -0.64248 FALSE
10 -1.1948 FALSE
30 -0.54501 FALSE

80 1.079462 FALSE
75 0.917015 FALSE
40 -0.22012 FALSE
35 -0.38256 FALSE
10 -1.1948 FALSE
25 -0.70746 FALSE
10 -1.1948 FALSE
15 -1.03235 FALSE
70 0.754567 FALSE
75 0.917015 FALSE
78 1.014483 FALSE
79 1.046973 FALSE
16 -0.99986 FALSE
17 -0.96737 FALSE
40 -0.22012 FALSE
35 -0.38256 FALSE
14 -1.06484 FALSE
13 -1.09733 FALSE
24 -0.73995 FALSE
23 -0.77244 FALSE
20 -0.86991 FALSE
15 -1.03235 FALSE
5 -1.35725 FALSE
7 -1.29227 FALSE
10 -1.1948 FALSE
25 -0.70746 FALSE
30 -0.54501 FALSE
35 -0.38256 FALSE
32 -0.48003 FALSE
25 -0.70746 FALSE
72 0.819546 FALSE
75 0.917015 FALSE
20 -0.86991 FALSE
10 -1.1948 FALSE
90 1.404356 FALSE
80 1.079462 FALSE
80 1.079462 FALSE
78 1.014483 FALSE
10 -1.1948 FALSE
10 -1.1948 FALSE
98 1.664272 FALSE
75 0.917015 FALSE
10 -1.1948 FALSE

35 -0.38256 FALSE
10 -1.1948 FALSE
5 -1.35725 FALSE
10 -1.1948 FALSE
35 -0.38256 FALSE
20 -0.86991 FALSE
32 -0.48003 FALSE
10 -1.1948 FALSE
12 -1.12982 FALSE
11 -1.16231 FALSE
10 -1.1948 FALSE
69 0.722078 FALSE
70 0.754567 FALSE
89 1.371867 FALSE
79 1.046973 FALSE
15 -1.03235 FALSE
20 -0.86991 FALSE
4 -1.38974 FALSE
5 -1.35725 FALSE
88 1.339378 FALSE
90 1.404356 FALSE
86 1.274399 FALSE
90 1.404356 FALSE
78 1.014483 FALSE
70 0.754567 FALSE
80 1.079462 FALSE
85 1.241909 FALSE
88 1.339378 FALSE
89 1.371867 FALSE
39 -0.25261 FALSE
35 -0.38256 FALSE
76 0.949504 FALSE
65 0.59212 FALSE
96 1.599293 FALSE
80 1.079462 FALSE
2 -1.45472 FALSE
3 -1.42223 FALSE
50 0.104778 FALSE
53 0.202247 FALSE
70 0.754567 FALSE
59 0.397184 FALSE
78 1.014483 FALSE
79 1.046973 FALSE

10 -1.1948 FALSE
9 -1.22729 FALSE
98 1.664272 FALSE
89 1.371867 FALSE
88 1.339378 FALSE
99 1.696762 FALSE
82 1.144441 FALSE
84 1.20942 FALSE
70 0.754567 FALSE
74 0.884525 FALSE
90 1.404356 FALSE
84 1.20942 FALSE
80 1.079462 FALSE
81 1.111951 FALSE
10 -1.1948 FALSE
11 -1.16231 FALSE
85 1.241909 FALSE
80 1.079462 FALSE
95 1.566804 FALSE
87 1.306888 FALSE
85 1.241909 FALSE
79 1.046973 FALSE
80 1.079462 FALSE
70 0.754567 FALSE
80 1.079462 FALSE
70 0.754567 FALSE
89 1.371867 FALSE
90 1.404356 FALSE
69 0.722078 FALSE
70 0.754567 FALSE
75 0.917015 FALSE
72 0.819546 FALSE
77 0.981994 FALSE
71 0.787057 FALSE
87 1.306888 FALSE
81 1.111951 FALSE
15 -1.03235 FALSE
19 -0.90239 FALSE
25 -0.70746 FALSE
29 -0.5775 FALSE
45 -0.05767 FALSE
39 -0.25261 FALSE
85 1.241909 FALSE

79 1.046973 FALSE
90 1.404356 FALSE
80 1.079462 FALSE
80 1.079462 FALSE
71 0.787057 FALSE
72 0.819546 FALSE
69 0.722078 FALSE
85 1.241909 FALSE
89 1.371867 FALSE
80 1.079462 FALSE
87 1.306888 FALSE
15 -1.03235 FALSE
9 -1.22729 FALSE
81 1.111951 FALSE
78 1.014483 FALSE
80 1.079462 FALSE
85 1.241909 FALSE
2 -1.45472 FALSE
5 -1.35725 FALSE
50 0.104778 FALSE
55 0.267226 FALSE
30 -0.54501 FALSE
35 -0.38256 FALSE
Mean SD
COUNT
TRUES
46.775 30.77922 0
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.
Marks Topic
80 Religion
55 Religion
95 Religion
90 Religion
90 Religion
79 Religion
91 Religion
84 Religion

42 Religion
46 Religion
77 Religion
100 Religion
61 Religion
87 Religion
91 Religion
80 Religion
70 Religion
95 Religion
99 Religion
54 Religion
 N = 20
 Mean value = 70
 Standard deviation = 17.8
 Standard error = 17.8 / square root of 20
= 17.8 / 4.47
= 3.98
Upper confidence interval level
Mean value = +t * standard error
= 78.3 + 1.96 * 3.98
= 319.78
Lower interval confidence level
Mean value = - t * standard error
= 78.3 - 1.96 * 3.98
= 304.16
Identifying the level to which mean value is above 70
H0: μ = 70
H1: μ > 70
(Mean value – μ) / (standard deviation /square root of n
= (78.3 – 70) / (17.8 / 4.47)
= 8.3 / 3.98
= 2.08

The above depicted aspect presents that mean value is greater than 0.05 so it can be said
that null hypothesis is accepted and other one is rejected. In other words, it can be presented that
students who enrolled in religion got marks equal to 70.
(G) Multiple linear regression
Regression Statistics
Multiple R 0.712984668
R Square 0.508347137
Adjusted R Square 0.498932508
Standard Error 12.41928686
Observations 480
ANOVA
df SS MS F
Significance
F
Regression 9 74953.68421 8328.187 53.99544917 5.82E-67
Residual 470 72492.18246 154.2387
Total 479 147445.8667
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 45.1997629 3.371279415 13.4073 6.15226E-35 38.57512
raisedhands 0.139597398 0.028235744 4.943996 1.0669E-06 0.084113
VisITedResources 0.209948563 0.025368693 8.275892 1.32896E-15 0.160098
AnnouncementsView 0.091943139 0.031884255 2.883653 0.00411128 0.02929
Discussion 0.037434311 0.023484091 1.594029 0.111601869 -0.00871
Female 4.938478092 1.220771196 4.045376 6.10582E-05 2.539633
Math 8.865062047 3.224790353 2.749035 0.006207287 2.528271
Science 4.085438573 3.079478632 1.326666 0.18526352 -1.96581
Language 7.989265312 3.065987078 2.605773 0.009457573 1.964527
Religion 2.676533075 3.929467718 0.681144 0.496115876 -5.04497
(H) Coefficient estimate for raised hands
H0: There is no significant mean difference between variable marks and raising hands.
H1: There is significant mean difference between variable marks and raising hands.
It can be seen from the table given above that coefficient of the variable raised hand is
0.13 and value of level of significance is 1.06. This means that there is no significant difference

between the dependent variable which is marks and raised hands as value of level of significance
is 1.06>0.05. Slope value 0.13 reflects that with slight change in the variable raised hands in
class marks gained changed by 0.13 points.
(I)Interpretation of slope coefficients
Results are reflecting that slope value of visited resources is 0.20 which means with
change in visited resources marks changed by 0.20 points followed by variation in marks cause
by 0.09 point in case of announcement views, 0.03 in case of discussion. If one focus on math’s
then marks changed by 8.86 points, followed by 4.08 in case of science. In case of language
marks change by 7.9 points and in case of religion same changed by 2.67 points. Results are up
to expected level as it was anticipation that in case students asked questions to teachers and
visited more resources big change will come in marks in comparison to other options. This hunch
proved correct by results. It was expectation that marks will be high in math’s in comparison to
science because former one is practical subject and students merely by looking at figures easily
understand lots of things and by practicing become master on same. This expectation also proved
correct by results. Students have expertise in specific language and it was expectation that same
largely contribute to earnings of marks. This hunch is also proved correct by high coefficient
value which is 7.98.
(J) R square and adjusted R square
Value of R square is 0.50 and adjusted R square is 0.49 which means that with change in
independent variables 50% variation comes in dependent variable which is marks. Adjusted R
square is reflecting that in case any variable will be added in the model then with change in
independent variable marks will change by 0.49%. There is little difference between R square
and adjusted R square because all variables are considered in the model and only history variable
is excluded. Single mentioned variable cannot largely affect the results of model. Hence, there is
no big difference between values of R square and adjusted R square.
(K) Statistical significance of model
Level of significance of model is 5.82>0.05 which means that there is no big statistical
difference between marks and independent variables.

(L) Variables that can be taken in to consideration
Apart from above mentioned variables students presence in class is the variable that can
be include in the model to identify its impact on marks.
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.
Regression helps to determine or predict the dependent variable by creating a regression equation
upon independent variables.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.713043
R Square 0.50843
Adjusted R Square 0.495816
Standard Error 12.43148
Observations 480
ANOVA
df SS MS F Significance F
Regression 11 74965.85 6815.077 48.50852 2.62E-70
Residual 469 72480.02 154.5416
Total 480 147445.9
Coeffic
ients
Standard
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
47.428
06 3.415724
13.88
521
5.77E
-37
40.716
04
54.140
08
40.7160
4
54.1400
8
GradeID
0.0612
27 0.218215
0.280
581
0.779
156
-
0.3675
7
0.4900
26
-
0.36757
0.49002
6
raisedhands
0.1387
2 0.028436
4.878
35
1.47E
-06
0.0828
43
0.1945
98
0.08284
3
0.19459
8

VisITedResou
rces
0.2108
15 0.02558
8.241
232
1.72E
-15
0.1605
48
0.2610
81
0.16054
8
0.26108
1
Announcemen
tsView
0.0917
14 0.031926
2.872
7
0.004
254
0.0289
78
0.1544
5
0.02897
8 0.15445
Discussion
0.0367
92 0.023618
1.557
755
0.119
966
-
0.0096
2
0.0832
03
-
0.00962
0.08320
3
Female
4.9567
04 1.223695
4.050
605
5.98E
-05
2.5521
01
7.3613
06
2.55210
1
7.36130
6
Math
6.3696
38 3.036658
2.097
582
0.036
477 0.4025
12.336
78 0.4025
12.3367
8
Science
1.4676
1 2.88342
0.508
983
0.611
004
-
4.1984
1
7.1336
31
-
4.19841
7.13363
1
Language
5.4755
86 2.866693
1.910
07
0.056
734
-
0.1575
7
11.108
74
-
0.15757
11.1087
4
Religion 0 0
6553
5
#NU
M! 0 0 0 0
History
-
2.5894
6 3.945547
-
0.656
3
0.511
953
-
10.342
6
5.1636
76
-
10.3426
5.16367
6
Predicted regression equation: 47 + 0.06*(grade) + 0.13*(raise hand)+0.21*(Visited resources)
+0.09*(Announcement) + 0.036*(Discussion) + 4.95*(female) + 6.36(Maths)
Predicted marks: 47 + 0.06(6) + 0.13(35) + 0.21(40) + 0.09*(75) + 0.036(5) + 4.95(1) +
6.36(1)
In the given equation, the marks of the candidate is an intercept(dependent variable) and
numbers from different coefficient of every independent variable like visited resources, raised
hand times, announcement, discussion and others. The equation cannot be considers here
appropriate because it also accounted year 6 by incorporating year 6 variable which is not right.

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.
There are various assumption that need to be considered by an individual while using
linear regression analysis that is highly based on the linear [predictive model using single
variable in order to determine the final outcome. It emphasises on various aspects covered in the
above question that it shows linear relationship, multivariate normality, little multicolinearity, no
correlation among the variable chosen for the analysis and homoscedasticity.
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.
Researcher needs to undertake random sampling process which in turn
helps in selecting suitable sample for the study. Moreover, such
sampling technique helps in getting unbiased results or output.

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?
Marks at least 90= 11
Total marks count= 480
Probability of not selecting students= (5/480)-(11/480)
= 0.10- 0.22
= -0.11