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Social Networking Tools And College Performance:
Social networking tools and college performance:
Introduction
The following is a report showing the relationship between social networks and college performance, the data set sample size is n =103 and the two variable include social networking time and performance. In order to show the relationship between the two variables social networking time is the independent variable while performance is the dependent variable.
Scatter diagram:
The following is a scatter diagram plot that shows the relationship between the two variables.
The trend line above shows a weak but positive relationship between the two variables, this relationship shows that as social networking time increases performance also increases. From the chart the estimated model is as follows:
Y = 73.051 + 0.0534 X, where Y is performance and X is social networking time. The slope value is 0.0534 meaning that if social networking time is increased by one unit holding all factors constant then the performance value will increase by 0.0534 units.
ANOVA table:
This table is the ANOVA table showing the sources of variation:
ANOVA
variation source
sum of squares
degrees of freedom
mean sum of squares
ess
23.81627594
1
23.81627594
rss
11394.68313
101
112.8186449
tss
11418.49941
103
110.8592176
The table above shows that the level of explained sum of squares is relatively low compared to the total sum of squares and residual sum of squares, the R squared value is calculated as follows r squared = ess/tss and results show that the R squared value is equal to 0.0021, this R squared value shows the deviations of the dependent variable that are explained by the independent variable, in this case only 0.21% of deviations in performance is explained by social networking time, this means that there is a weak relationship between the two variable.
Statistical significance of the estimated values:
In order to determine whether the two estimated values are statistically significant the F test is undertaken,
hypothesis:
Ho: A= B = 0
Ha: A ≠ B ≠ 0
Where a is the constant value estimated, B is the slope value.
F statistics value is calculated as follows:
F = (ESS/ D.F)/ (RSS/ D.F)
Using the ANOVA table the F value is
F = (23.81627594)/ (112.8186449)
F =0.211102305
F test alpha = 0.05
P value 3.8415
The P value > F calculated
This means the null hypothesis that A= B = 0 is accepted and therefore the estimates are not statistically significant.
The above model is not appropriate for forecasting purposes, this is because although there is a relationship between the two variables performance cannot entirely be explained by social networking time only, there are other factors that affect performance which are not included in the model and this is the reason why the residual value is relatively high and the R squared value relatively low.
The chart below shows the standardized residual plot:
From the chart there are a number of outliers that are greater than the value 3 and 2, this can be as a result of inconsistencies in data collected. However this can also be as a result the nature of human behavior which is sometimes unpredictable, respondents with values that are outliers should verify whether information they provided is correct and whether there are other activities they feel affect their performance.
Conclusion:
The estimated model depicts the relationship between social networking time and performance, results show that there is a positive relationship between the two variables, however the R squared values show a weak relationship where only a small percentage of deviation in performance is explained by social networking time, the F test that establishes the statistical significance of the estimated parameters show that the estimates are not statistically significant and therefore the model is not appropriate for forecasting purposes.
Reference:
Mendenhall, W. (2003) Introduction to statistics, Prentice Hall press, New Jersey
Appendixes:
X
Y
Y est
Social networking time (hrs)
Performance (pts so far)
y
x
xy
x2
estimated Y
e
e2
tss
ess
standardized residual
13
65.50
-8.14
2.00
-16.24
3.98
73.75
-8.25
67.98
66.24
0.01
-0.24
11
72.00
-1.64
0.00
0.01
0.00
73.64
-1.64
2.68
2.69
0.00
-0.60
6
67.00
-6.64
-5.00
33.22
25.04
73.37
-6.37
40.59
44.07
0.07
-0.39
12.5
71.50
-2.14
1.50
-3.20
2.24
73.72
-2.22
4.92
4.57
0.01
-0.59
3
66.75
-6.89
-8.00
55.14
64.07
73.21
-6.46
41.74
47.45
0.18
-0.38
11
66.50
-7.14
0.00
0.03
0.00
73.64
-7.14
50.96
50.96
0.00
-0.33
5
70.50
-3.14
-6.00
18.85
36.05
73.32
-2.82
7.94
9.85
0.10
-0.57
12
86.00
12.36
1.00
12.31
0.99
73.69
12.31
151.49
152.80
0.00
0.23
4
86.75
13.11
-7.00
-91.84
49.06
73.26
13.49
181.86
171.91
0.14
0.39
24
76.00
2.36
13.00
30.69
168.89
74.33
1.67
2.78
5.58
0.48
-0.60
29
71.00
-2.64
18.00
-47.48
323.84
74.60
-3.60
12.96
6.96
0.92
-0.54
1
73.50
-0.14
-10.00
1.39
100.09
73.10
0.40
0.16
0.02
0.29
-0.61
6
76.00
2.36
-5.00
-11.82
25.04
73.37
2.63
6.91
5.58
0.07
-0.57
3.5
71.50
-2.14
-7.50
16.05
56.32
73.24
-1.74
3.02
4.57
0.16
-0.60
5.8
82.00
8.36
-5.20
-43.52
27.09
73.36
8.64
74.64
69.91
0.08
-0.20
46
70.00
-3.64
35.00
-127.34
1224.69
75.51
-5.51
30.34
13.24
3.50
-0.44
18
46.00
-27.64
7.00
-193.35
48.94
74.01
-28.01
784.69
763.89
0.14
3.73
5.5
65.58
-8.06
-5.50
44.36
30.30
73.34
-7.76
60.29
64.94
0.09
-0.28
6.5
56.50
-17.14
-4.50
77.20
20.29
73.40
-16.90
285.54
293.73
0.06
0.97
13
79.00
5.36
2.00
10.70
3.98
73.75
5.25
27.61
28.74
0.01
-0.46
7.1
54.50
-19.14
-3.90
74.72
15.24
73.43
-18.93
358.35
366.29
0.04
1.37
7
37.00
-36.64
-4.00
146.71
16.03
73.42
-36.42
1326.76
1342.39
0.05
6.74
23
56.50
-17.14
12.00
-205.59
143.90
74.28
-17.78
316.11
293.73
0.41
1.14
13
49.50
-24.14
2.00
-48.17
3.98
73.75
-24.25
587.83
582.67
0.01
2.64
3
78.75
5.11
-8.00
-40.91
64.07
73.21
5.54
30.68
26.13
0.18
-0.44
5.2
66.75
-6.89
-5.80
39.98
33.69
73.33
-6.58
43.28
47.45
0.10
-0.37
1.1
74.50
0.86
-9.90
-8.53
98.10
73.11
1.39
1.93
0.74
0.28
-0.60
11.1
71.00
-2.64
0.10
-0.25
0.01
73.64
-2.64
6.99
6.96
0.00
-0.57
17
83.00
9.36
6.00
56.13
35.95
73.96
9.04
81.74
87.64
0.10
-0.16
7.5
67.75
-5.89
-3.50
20.64
12.28
73.45
-5.70
32.51
34.68
0.04
-0.43
3.1
82.75
9.11
-7.90
-72.02
62.48
73.22
9.53
90.89
83.02
0.18
-0.11
11.5
64.25
-9.39
0.50
-4.65
0.25
73.67
-9.42
88.64
88.15
0.00
-0.12
12.7
67.75
-5.89
1.70
-9.98
2.88
73.73
-5.98
35.75
34.68
0.01
-0.41
9.75
77.50
3.86
-1.25
-4.84
1.57
73.57
3.93
15.43
14.91
0.00
-0.53
14
76.50
2.86
3.00
8.57
8.97
73.80
2.70
7.30
8.19
0.03
-0.57
13.5
72.00
-1.64
2.50
-4.09
6.23
73.77
-1.77
3.14
2.69
0.02
-0.60
33
83.75
10.11
22.00
222.41
483.81
74.81
8.94
79.86
102.24
1.38
-0.17
18.2
83.00
9.36
7.20
67.36
51.78
74.02
8.98
80.59
87.64
0.15
-0.17
26
74.00
0.36
15.00
5.42
224.87
74.44
-0.44
0.19
0.13
0.64
-0.61
6.5
64.50
-9.14
-4.50
41.16
20.29
73.40
-8.90
79.17
83.51
0.06
-0.17
17.5
53.50
-20.14
6.50
-130.81
42.19
73.99
-20.49
419.66
405.56
0.12
1.71
21
75.25
1.61
10.00
16.11
99.91
74.17
1.08
1.16
2.60
0.29
-0.61
8
50.00
-23.64
-3.00
71.02
9.03
73.48
-23.48
551.22
558.79
0.03
2.44
5.1
73.42
-0.22
-5.90
1.29
34.86
73.32
0.10
0.01
0.05
0.10
-0.61
13.5
87.00
13.36
2.50
33.35
6.23
73.77
13.23
174.98
178.53
0.02
0.36
14
76.25
2.61
3.00
7.82
8.97
73.80
2.45
6.01
6.82
0.03
-0.58
7.5
63.50
-10.14
-3.50
35.53
12.28
73.45
-9.95
99.03
102.79
0.04
-0.06
22.5
85.75
12.11
11.50
139.23
132.15
74.25
11.50
132.19
146.69
0.38
0.12
15
78.50
4.86
4.00
19.42
15.97
73.85
4.65
21.60
23.63
0.05
-0.49
61
82.00
8.36
50.00
418.03
2499.56
76.31
5.69
32.38
69.91
7.13
-0.43
3.75
84.00
10.36
-7.25
-75.17
52.63
73.25
10.75
115.54
107.36
0.15
0.03
4
54.00
-19.64
-7.00
137.56
49.06
73.26
-19.26
371.12
385.68
0.14
1.44
13
59.50
-14.14
2.00
-28.22
3.98
73.75
-14.25
202.93
199.90
0.01
0.51
7
84.25
10.61
-4.00
-42.49
16.03
73.42
10.83
117.19
112.60
0.05
0.04
2.5
55.00
-18.64
-8.50
158.51
72.32
73.18
-18.18
330.67
347.40
0.21
1.22
3.1
78.50
4.86
-7.90
-38.43
62.48
73.22
5.28
27.92
23.63
0.18
-0.46
9.8
81.25
7.61
-1.20
-9.17
1.45
73.57
7.68
58.92
57.93
0.00
-0.29
12
87.00
13.36
1.00
13.30
0.99
73.69
13.31
177.11
178.53
0.00
0.37
7.1
73.00
-0.64
-3.90
2.49
15.24
73.43
-0.43
0.18
0.41
0.04
-0.61
11
82.00
8.36
0.00
-0.04
0.00
73.64
8.36
69.92
69.91
0.00
-0.23
4
67.00
-6.64
-7.00
46.50
49.06
73.26
-6.26
39.24
44.07
0.14
-0.40
30
75.00
1.36
19.00
25.86
360.83
74.65
0.35
0.12
1.85
1.03
-0.61
20
65.00
-8.64
9.00
-77.71
80.92
74.12
-9.12
83.16
74.63
0.23
-0.15
2
84.75
11.11
-9.00
-100.05
81.08
73.16
11.59
134.38
123.46
0.23
0.13
7.5
80.50
6.86
-3.50
-24.04
12.28
73.45
7.05
49.68
47.08
0.04
-0.34
27
83.50
9.86
16.00
157.74
255.86
74.49
9.01
81.12
97.25
0.73
-0.16
12
79.50
5.86
1.00
5.84
0.99
73.69
5.81
33.73
34.36
0.00
-0.43
9
84.00
10.36
-2.00
-20.77
4.02
73.53
10.47
109.59
107.36
0.01
-0.01
2.75
74.50
0.86
-8.25
-7.11
68.13
73.20
1.30
1.70
0.74
0.19
-0.60
7
78.00
4.36
-4.00
-17.46
16.03
73.42
4.58
20.93
19.02
0.05
-0.50
5.5
87.50
13.86
-5.50
-76.30
30.30
73.34
14.16
200.38
192.14
0.09
0.50
3.7
63.00
-10.64
-7.30
77.71
53.35
73.25
-10.25
105.03
113.18
0.15
-0.03
5.5
83.00
9.36
-5.50
-51.53
30.30
73.34
9.66
93.23
87.64
0.09
-0.10
9
62.00
-11.64
-2.00
23.33
4.02
73.53
-11.53
132.98
135.46
0.01
0.12
9
88.00
14.36
-2.00
-28.79
4.02
73.53
14.47
209.34
206.25
0.01
0.55
1.1
74.50
0.86
-9.90
-8.53
98.10
73.11
1.39
1.93
0.74
0.28
-0.60
13
77.50
3.86
2.00
7.71
3.98
73.75
3.75
14.10
14.91
0.01
-0.53
13
77.50
3.86
2.00
7.71
3.98
73.75
3.75
14.10
14.91
0.01
-0.53
10
87.00
13.36
-1.00
-13.42
1.01
73.58
13.42
179.96
178.53
0.00
0.38
5.5
70.00
-3.64
-5.50
20.03
30.30
73.34
-3.34
11.19
13.24
0.09
-0.55
6
76.50
2.86
-5.00
-14.32
25.04
73.37
3.13
9.79
8.19
0.07
-0.56
6
71.50
-2.14
-5.00
10.70
25.04
73.37
-1.87
3.50
4.57
0.07
-0.59
11
72.25
-1.39
0.00
0.01
0.00
73.64
-1.39
1.93
1.93
0.00
-0.60
3
82.00
8.36
-8.00
-66.93
64.07
73.21
8.79
77.25
69.91
0.18
-0.18
14
76.50
2.86
3.00
8.57
8.97
73.80
2.70
7.30
8.19
0.03
-0.57
3.5
76.00
2.36
-7.50
-17.72
56.32
73.24
2.76
7.63
5.58
0.16
-0.57
1.1
89.00
15.36
-9.90
-152.14
98.10
73.11
15.89
252.51
235.97
0.28
0.79
14
77.00
3.36
3.00
10.07
8.97
73.80
3.20
10.25
11.30
0.03
-0.56
4
64.50
-9.14
-7.00
64.01
49.06
73.26
-8.76
76.82
83.51
0.14
-0.19
11
69.50
-4.14
0.00
0.02
0.00
73.64
-4.14
17.13
17.13
0.00
-0.52
8
55.20
-18.44
-3.00
55.40
9.03
73.48
-18.28
334.09
339.98
0.03
1.24
7
83.00
9.36
-4.00
-37.49
16.03
73.42
9.58
91.69
87.64
0.05
-0.10
7.5
83.58
9.94
-3.50
-34.84
12.28
73.45
10.13
102.59
98.83
0.04
-0.04
5.5
83.50
9.86
-5.50
-54.28
30.30
73.34
10.16
103.13
97.25
0.09
-0.04
13.5
64.00
-9.64
2.50
-24.05
6.23
73.77
-9.77
95.49
92.90
0.02
-0.08
10
76.00
2.36
-1.00
-2.37
1.01
73.58
2.42
5.83
5.58
0.00
-0.58
19.4
85.50
11.86
8.40
99.58
70.49
74.09
11.41
130.25
140.69
0.20
0.11
5.5
87.00
13.36
-5.50
-73.55
30.30
73.34
13.66
186.47
178.53
0.09
0.42
10.5
76.00
2.36
-0.50
-1.19
0.25
73.61
2.39
5.70
5.58
0.00
-0.58
9.5
79.00
5.36
-1.50
-8.07
2.26
73.56
5.44
29.61
28.74
0.01
-0.45
8
87.00
13.36
-3.00
-40.14
9.03
73.48
13.52
182.84
178.53
0.03
0.40
11
85.00
11.36
0.00
-0.05
0.00
73.64
11.36
129.09
129.08
0.00
0.10
10.5
75.00
1.36
-0.50
-0.69
0.25
73.61
1.39
1.93
1.85
0.00
-0.60
total
1133.45
7584.78
0.00
0.00
445.79
8344.23
0.00
11394.68
11418.50
23.82
mean
11.00436893
73.64
0.00
110.63
stdev
180.53
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