Question

In: Statistics and Probability

Predicting High/Low user of Social Networking Sites among students A study was conducted to identify the...

Predicting High/Low user of Social Networking Sites among students

A study was conducted to identify the variables which distinguish between heavy/light users of social networking sites among students. A questionnaire was designed for the purpose. The social networking sites considered for the study were Facebook, Orkut, Linked-in, Twitter, etc. the online survey was conducted on a sample of 61 students in the age group of 20 to 30. The collected response data is attached herewith in excel sheet.

DATA Reference:

Resp. No. X1 X2 X3A X3B X3C X3D X3E X3F X3G X3H X3I X3J X3K X3L
1 2 3 1 2 3 5 2 3 2 5 4 2 2 1
2 4 3 4 4 5 2 2 3 4 2 2 4 4 1
3 2 3 1 5 3 2 2 5 3 1 1 4 1 1
4 2 3 5 4 5 3 4 5 5 4 5 5 3 3
5 2 2 4 4 5 4 3 3 3 2 3 4 3 2
6 2 2 2 4 5 1 1 2 2 1 2 3 2 1
7 1 2 2 2 3 1 1 1 2 1 1 3 2 1
8 4 1 5 3 3 2 2 2 2 2 2 5 5 1
9 2 2 3 5 4 4 4 3 2 4 5 5 3 2
10 1 1 3 5 5 1 3 2 1 1 2 4 2 1
11 1 1 5 1 2 5 3 3 3 4 4 2 5 5
12 4 1 3 4 4 3 3 3 3 3 3 4 4 2
13 2 2 5 4 4 2 5 3 3 2 2 4 3 1
14 1 1 5 1 1 5 5 5 3 5 3 3 5 5
15 1 1 3 4 5 1 3 4 4 3 3 4 1 1
16 1 1 5 1 1 2 5 5 5 5 3 5 5 5
17 1 1 1 4 4 4 4 2 2 1 1 4 1 2
18 2 2 3 2 4 1 4 2 4 5 3 5 3 1
19 4 1 2 3 2 2 2 2 3 4 4 3 2 2
20 1 1 5 4 4 2 1 1 1 1 5 4 1 5
21 3 1 3 4 5 4 4 4 3 3 2 2 3 4
22 1 1 2 4 5 1 2 2 2 3 3 5 3 1
23 3 1 4 5 5 5 4 4 3 3 3 5 4 3
24 1 1 3 5 5 4 4 4 5 5 5 5 3 3
25 1 1 2 3 3 3 3 3 3 3 3 4 2 1
26 1 1 4 4 4 3 3 3 3 1 3 4 2 2
27 1 1 4 4 5 3 4 4 4 4 5 5 5 3
28 3 2 4 4 4 4 4 4 4 4 4 4 4 1
29 2 2 2 3 4 2 3 4 4 4 3 2 2 1
30 1 3 4 4 4 4 4 5 4 4 5 5 2 4
31 1 1 4 4 5 2 5 3 5 2 5 5 3 1
32 2 2 3 4 4 4 2 2 2 2 2 2 2 2
33 1 2 3 1 2 4 4 3 2 2 4 2 1 1
34 1 1 4 4 5 4 3 3 3 4 4 4 3 4
35 1 4 1 4 4 5 4 4 3 4 3 4 4 5
36 2 4 2 3 3 4 4 3 4 3 4 4 3 5
37 2 3 3 2 3 3 4 4 4 5 4 5 2 4
38 2 3 1 3 3 4 3 3 3 4 3 4 3 4
39 1 3 1 4 4 5 2 3 2 2 3 5 3 5
40 2 3 1 2 3 3 3 4 4 4 4 5 4 4
41 2 3 2 3 4 3 5 5 4 4 5 4 3 3
42 1 3 4 1 1 1 3 2 1 1 4 2 4 3
43 2 3 2 2 3 4 4 4 3 3 3 4 2 4
44 1 2 2 2 4 3 2 2 3 4 1 4 2 4
45 4 4 4 1 1 2 3 2 1 2 5 3 4 4
46 1 3 1 3 4 3 4 3 4 4 3 4 3 3
47 1 1 1 5 5 5 1 1 1 1 1 5 1 1
48 1 2 1 2 3 3 2 2 3 3 2 3 2 3
49 1 2 1 2 3 3 2 2 3 3 2 4 3 4
50 1 2 1 2 3 4 3 2 3 4 2 4 2 4
51 1 1 5 3 3 4 2 2 3 3 2 4 4 2
52 2 2 4 5 4 4 4 4 2 3 3 4 4 5
53 2 1 4 3 4 4 3 2 3 3 3 4 3 3
54 4 4 4 4 4 4 3 3 3 3 3 3 3 3
55 4 4 1 5 5 5 5 5 1 5 1 5 1 5
56 4 4 2 4 4 3 3 2 2 5 2 4 2 5
57 1 2 2 3 4 4 2 2 2 3 2 4 4 4
58 1 3 2 4 4 4 2 2 2 4 3 5 4 4
59 1 2 2 4 4 5 2 2 3 4 3 5 3 4
60 1 4 2 4 4 4 1 2 3 4 3 5 3 4
61 1 2 1 5 5 5 2 2 3 4 3 4 2 3
X1 = Time spent on week days
1 = Less than 1 Hr
2 = 1 to less than 3 hours
3 = 3 to less than 5 hours
4 = More than 5 hrs
X2 = Time spent on week ends
1 = Less than 2 hrs
2 = 2 to less than 4 hours
3 = 4-6 hrs
4 = More than 6 hrs
X3A = Linking with Professional
X3B = Messaging
X3C = Networking
X3D = Make new friends
X3E = Promote events
X3F = Blogging
X3G = News Updates
X3H = Games
X3I = Education
X3J = Photo sharing
X3K = Job seeking
X3L = Online dating

For questions X3A to X3L, 1 = least useful and 5 = extremely useful

Questions:

Q1. Divide the sample into two groups-one that is using the social networking site for less than one hour on weekdays (low users) and the second which is using the social networking site for one or more hours (high users). Run a two-group Logistic regression analysis with high/low user as a categorical dependent variable and the variables X3A to X3L as predictor variables. To:

a. Compute the percentage of respondents that it is able to classify correctly

b. Determine the statistical significance of the logistic function

c. Identify which of the predictor variables are relatively better in classifying between the two groups.

d. Classify a new respondent into one the two groups by building a decision rule and a cut-off score.

e. Explain the odds ratios in the SPSS output

Q2. Divide the sample into two groups-one that is using the social networking site for less than four hours on weekends(low users) and the second which is using the social networking site for four or more hours on weekends(high users) and repeat the analysis as carried out in the first question.

Solutions

Expert Solution

I do not have SPSS, so I have used EXCEL to solve the question. First of all, one needs to install Real statistics resource pack as AddIn to Excel which has Logistic Regression solver.

a) Compute the percentage of respondents that it is able to classify correctly.

The result of the classification table inserted below shows us numbers of classifications classified correctly and incorrectly.

Classification Table
Suc-Obs Fail-Obs SUM
Suc-Pred 19 11 30
Fail-Pred 10 21 31
SUM 29 32 61

The table has values categorized as follows:

Classification Table
Suc-Obs Fail-Obs
Suc-Pred TP FP
Fail-Pred FN TN

True Positives (TP) = the number of cases which were correctly classified to be positive, i.e. were predicted to be a success and were actually observed to be a success

False Positives (FP) = the number of cases which were incorrectly classified as positive, i.e. were predicted to be a success but were actually observed to be a failure

True Negatives (TN) = the number of cases which were correctly classified to be negative, i.e. were predicted to be a failure and were actually observed to be a failure

False Negatives (FN) = the number of cases which were incorrectly classified as negative, i.e. were predicted to be a negative but were actually observed to be a success.

Percentage of respondents that it is able to classify correctly = (TP+TN/Total)*100 = ((19+21)/61)*100 = 65.37%

b. Determine the statistical significance of the logistic function

LL0 -42.2082
LL1 -35.9327
Chi-Sq 12.55094
df 12
p-value 0.402506
alpha 0.05
sig no

From the analysis, we get the significance test values as given in the table. The coefficient of the logistic regressions a = -42.2 and b = -35.9

The logistic regression model is given as

c. Identify which of the predictor variables are relatively better in classifying between the two groups.

coeff b s.e. Wald p-value exp(b) lower upper
Intercept -0.14963 1.820771 0.006753 0.934505 0.861029
X3A -0.0146 0.281978 0.002682 0.958695 0.985502 0.567071 1.712685
X3B 0.559262 0.498285 1.259722 0.261704 1.749381 0.658784 4.645424
X3C -0.1649 0.503224 0.107385 0.743141 0.847974 0.316255 2.27367
X3D -0.29475 0.296051 0.991247 0.319438 0.744716 0.416861 1.330423
X3E 0.146831 0.392836 0.139706 0.708574 1.158159 0.536272 2.501215
X3F 0.604464 0.446656 1.831451 0.175956 1.830272 0.762643 4.39248
X3G -0.36108 0.42638 0.717155 0.397079 0.696923 0.302169 1.607387
X3H 0.461482 0.338309 1.86073 0.172541 1.586424 0.817429 3.078848
X3I -0.07459 0.300851 0.061477 0.804177 0.92812 0.514659 1.673743
X3J -0.59604 0.401764 2.200962 0.137925 0.550987 0.250703 1.210944
X3K 0.221605 0.339166 0.426908 0.51351 1.248078 0.642012 2.426275
X3L -0.31477 0.27987 1.264982 0.26071 0.729954 0.421765 1.263342

None of the predictor is significantly above to differntitae the high and low users.(p value in the table aobe)


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