Fundamental Concepts And Techniques Of Data Analytics

Introduction to Data Analytics

It is important to check the relationship exists between the different variables, because this will allow us to know the nature of relationship and based on this relationship we can take further decisions about the dependent and independent variables. Checking relationship for prediction purpose is very important because it will help in deciding different policies. Here, we have to see the relationship exists between the three variables such as Child Qualities: Feeling of Responsibility, Family Important, and Work Important. For this study, we assume two independent variables as family important and work important and dependent variable as Child qualities: feeling of responsibility. By using different statistical tools and techniques we have to find out the correlation coefficients and then we have to check whether these correlation coefficients are statistically significant or not. For checking these significant relationships we have to use some statistical tools and techniques for the data analysis. Here, we have to use both techniques of determining the relationships. We have to use the parametric as well as non-parametric technique for finding the extent of relationship exists between the given variables. This means we will use Pearson’s correlation coefficient r and Spearman’s R correlation coefficient. Let us see this study in detail.

For this research study, we have to find out the relationship between the dependent variable child qualities: feeling of responsibility and independent variables family important and work important. First of all, we have to check whether there is any statistically significant relationship exists between the dependent variable child qualities: feeling of responsibility and independent variables family important. After checking this relationship we have to check whether there is any statistically significant relationship exists between the dependent variable child qualities: feeling of responsibility and independent variables work important. Dependent variable or response variable for this statistical study is given as below:

Dependent variable:  Child qualities: feeling of responsibility

The independent variables or predictors for this study are summarised as below:

Independent Variables: Family important, Work important

Now, we have to state two hypotheses based on above dependent and independent variables which are stated as below:

Hypothesis 1

Null hypothesis: H₀: There is no any statistically significant relationship exists between the two variables family important and child qualities: feeling of responsibility.

Alternative hypothesis: H_a: There is a statistically significant relationship exists between the two variable family important and child qualities: feeling of responsibility.

Hypothesis 2

Null hypothesis: H₀: There is no any statistically significant relationship exists between the two variables work important and child qualities: feeling of responsibility.

The Study Objectives

Alternative hypothesis: H_a: There is a statistically significant relationship exists between the two variable work important and child qualities: feeling of responsibility.

After checking above two hypotheses by using proper tests for relationships, if there is no sufficient evidence to conclude that there is statistically significant relationship exists between the dependent variable and independent variable, then we cannot use linear regression model. We know that given dependent variable is bivariate in nature i.e. this dependent variable or response variable have two responses and in this case we will use logistic regression model for the prediction of dependent variable child qualities: feeling of responsibility.

For this research study, we have to use a statistical data analysis by using SPSS statistical software. First we have to find out the frequency distributions for the given three variables and then we have to see the relationship exists between these variables by using the Pearson correlation coefficient and Spearman correlation coefficient. First of all we have to see the relationship between the dependent variable child qualities: feeling of responsibility and independent variable family important. After finding this relationship, we have to see the relationship between the dependent variable child qualities: feeling of responsibility and independent variable work important. We will use the corresponding P-values from the SPSS outputs for taking decisions regarding the null hypotheses. For both of the tests, we will consider 5% level of significance. We will take decision whether reject or do not reject the null hypothesis based on the comparison of P-value and alpha value.

If no statistically significant evidence of linear relationship exists between the given dependent and independent variables, then we cannot use linear regression model for the prediction of dependent variable. In this case, we will use other regression model. For the given data, dependent variable or response variable only have two values or two responses and hence we will use binary logistic regression model for the prediction of the dependent variable child qualities: feeling of responsibility.

Let us see this data analysis in detail given below.

In this section, we have to analyse the given data by using different tools and techniques of statistical analysis. We have to use SPSS for data analysis. First of all we have to see the frequency distributions for the given three variables Family important, Work important, and Child qualities: feeling of responsibility. For this study, we consider two independent variables as family important and work important. The dependent variable for this research study is Child qualities: feeling of responsibility. Now, we have to see the frequency distribution of the variable family important which is given as below:

Statistics
Family important
N	Valid	1038
Missing	3

Family important
	Frequency	Percent	Valid Percent	Cumulative Percent
Valid	Very important	981	94.2	94.5	94.5
Rather important	44	4.2	4.2	98.7
Not very important	10	1.0	1.0	99.7
Not at all important	3	.3	.3	100.0
Total	1038	99.7	100.0
Missing	Missing; Not asked by the interviewer	2	.2
No answer	1	.1
Total	3	.3
Total	1041	100.0

Relationships among Variables

From above frequency distribution table, it is observed that there are 3 missing values of total 1041 participants. For the question regarding to the variable family important, it is observed that most of the participants in the survey said that it is very important. About 981 respondents said that it is very important. It is observed that 44 respondents said that it is rather important, 10 respondents said that it is not very important, while 3 respondents said that not at all important.

This frequency distribution table concludes that about 94.5% of the respondents said that family is very important.

Now, we have to see the frequency distribution for the independent variable work important. The SPSS output for this frequency distribution is given as below:

Statistics
Work important
N	Valid	940
Missing	101

Work important
	Frequency	Percent	Valid Percent	Cumulative Percent
Valid	Very important	353	33.9	37.6	37.6
Rather important	365	35.1	38.8	76.4
Not very important	108	10.4	11.5	87.9
Not at all important	114	11.0	12.1	100.0
Total	940	90.3	100.0
Missing	Missing; Not asked by the interviewer	98	9.4
No answer	2	.2
Don´t know	1	.1
Total	101	9.7
Total	1041	100.0

There are about 101 missing values. Number of valid responses is 940. It is observed that about 353 respondents said that work is very important, 365 respondents said that work is rather important. About 108 respondents said that work is not very important. It is observed that about 114 respondents said that work is not at all important.

This table concludes that about 37.6% of the respondents said that work is very important.

Now, we have to see the frequency distribution for the variable Child qualities: feeling of responsibility. The SPSS output for this frequency distribution is given as below:

Statistics
Child qualities: feeling of responsibility
N	Valid	1041
Missing	0

Child qualities: feeling of responsibility
	Frequency	Percent	Valid Percent	Cumulative Percent
Valid	Mentioned	626	60.1	60.1	60.1
Not mentioned	415	39.9	39.9	100.0
Total	1041	100.0	100.0

From this table, it is observed that about 626 respondents were mention that child qualities regarding the feeling of responsibility. It is observed that about 415 respondents were not mention that child qualities regarding the feeling of responsibility.

Now, we have to see some correlational study for checking the relationship between the given three variables. We have to check two hypotheses which are given as below:

Hypothesis 1

Null hypothesis: H₀: There is no any statistically significant relationship exists between the two variables family important and child qualities: feeling of responsibility.

Alternative hypothesis: H_a: There is a statistically significant relationship exists between the two variable family important and child qualities: feeling of responsibility.

For this test, we consider 5% level of significance for checking the claim. The SPSS results for this test are given as below

Correlations
	Family important	Child qualities: feeling of responsibility
Family important	Pearson Correlation	1	.024
Sig. (2-tailed)		.441
N	1038	1038
Child qualities: feeling of responsibility	Pearson Correlation	.024	1
Sig. (2-tailed)	.441
N	1038	1041

From above SPSS output, it is observed that the Pearson correlation coefficient between two variables family important and child qualities: feeling of responsibility is given as 0.024. This indicates that there is a very low or negligible relationship or correlation exists between these two variables. The P-value for this relationship is given as 0.441 which is greater than alpha value 0.05, so we do not reject the null hypothesis that there is no any statistically significant relationship exists between the two variables family important and child qualities: feeling of responsibility.

Hypothesis Testing

There is insufficient evidence to conclude that there is a statistically significant relationship exists between the two variable family important and child qualities: feeling of responsibility.

Now, we have to see the non-parametric Spearman’s correlation coefficient between the given two variables. The SPSS output is given as below:

Correlations
	Family important	Child qualities: feeling of responsibility
Spearman’s rho	Family important	Correlation Coefficient	1.000	.020
Sig. (2-tailed)	.	.525
N	1038	1038
Child qualities: feeling of responsibility	Correlation Coefficient	.020	1.000
Sig. (2-tailed)	.525	.
N	1038	1041

From above output, it is observed that the correlation coefficient between these two variables is given as 0.02 which is negligible. P-value is given as 0.525. We do not reject the null hypothesis that there is no any statistically significant relationship exists between the two variables family important and child qualities: feeling of responsibility. There is insufficient evidence to conclude that there is a statistically significant relationship exists between the two variable family important and child qualities: feeling of responsibility.

Hypothesis 2

Null hypothesis: H₀: There is no any statistically significant relationship exists between the two variables work important and child qualities: feeling of responsibility.

Alternative hypothesis: H_a: There is a statistically significant relationship exists between the two variable work important and child qualities: feeling of responsibility.

For this test, we consider 5% level of significance for checking the claim. The SPSS results for this test are given as below:

Correlations
	Child qualities: feeling of responsibility	Work important
Child qualities: feeling of responsibility	Pearson Correlation	1	-.009
Sig. (2-tailed)		.779
N	1041	940
Work important	Pearson Correlation	-.009	1
Sig. (2-tailed)	.779
N	940	940

From above table, it is observed the Pearson correlation coefficient between the given two variables is given as -0.009 which is very low negative and negligible. The p-value for this test is given as 0.779. So, we do not reject the null hypothesis that there is a statistically significant relationship exists between the two variable work important and child qualities: feeling of responsibility.

There is insufficient evidence to conclude that there is a statistically significant relationship exists between the two variable work important and child qualities: feeling of responsibility.

Now, we have to check this relationship by using non-parametric Spearman correlation coefficient. Required SPSS output is given as below:

Correlations
	Child qualities: feeling of responsibility	Work important
Spearman’s rho	Child qualities: feeling of responsibility	Correlation Coefficient	1.000	-.012
Sig. (2-tailed)	.	.720
N	1041	940
Work important	Correlation Coefficient	-.012	1.000
Sig. (2-tailed)	.720	.
N	940	940

From this table, it is observed that the Spearman’s correlation coefficient is given as -0.012 which is negligible. P-value is given as 0.720 which is greater than alpha value 0.05. So, we do not reject the null hypothesis that there is a statistically significant relationship exists between the two variable work important and child qualities: feeling of responsibility. There is insufficient evidence to conclude that there is a statistically significant relationship exists between the two variable work important and child qualities: feeling of responsibility.

Now, we have to use the logistic regression model for the prediction of response variable child qualities: feeling of responsibility. Here, we have to use binary logistic model because dependent variable or response variable have only two types of responses such as ‘mentioned’ and ‘not mentioned’. Also, it is observed that the relationships between the dependent and independent variables are not statistically significant and therefore we cannot use linear models in this case. So, here we are using binary logistic regression model for the prediction of dependent or response variable child qualities: feeling of responsibility. The SPSS output for this regression model is given as below:

Case Processing Summary
Unweighted Casesa	N	Percent
Selected Cases	Included in Analysis	938	90.1
Missing Cases	103	9.9
Total	1041	100.0
Unselected Cases	0	.0
Total	1041	100.0
a. If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value	Internal Value
Mentioned	0
Not mentioned	1

Classification Tablea,b
	Observed	Predicted
	Child qualities: feeling of responsibility	Percentage Correct
	Mentioned	Not mentioned
Step 0	Child qualities: feeling of responsibility	Mentioned	561	0	100.0
Not mentioned	377	0	.0
Overall Percentage			59.8
a. Constant is included in the model.
b. The cut value is .500

Variables in the Equation
	B	S.E.	Wald	df	Sig.	Exp(B)
Step 0	Constant	-.397	.067	35.622	1	.000	.672

Variables not in the Equation
	Score	df	Sig.
Step 0	Variables	V4	.538	1	.463
V8	.095	1	.758
Overall Statistics	.645	2	.724

Omnibus Tests of Model Coefficients
	Chi-square	df	Sig.
Step 1	Step	.638	2	.727
Block	.638	2	.727
Model	.638	2	.727

Model Summary
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	1263.377a	.001	.001
a. Estimation terminated at iteration number 3 because parameter estimates changed by less than .001.

Classification Tablea
	Observed	Predicted
	Child qualities: feeling of responsibility	Percentage Correct
	Mentioned	Not mentioned
Step 1	Child qualities: feeling of responsibility	Mentioned	560	1	99.8
Not mentioned	375	2	.5
Overall Percentage			59.9
a. The cut value is .500

Variables in the Equation
	B	S.E.	Wald	df	Sig.	Exp(B)
Step 1a	V4	.154	.208	.547	1	.460	1.166
V8	-.022	.068	.108	1	.743	.978
Constant	-.518	.265	3.817	1	.051	.595
a. Variable(s) entered on step 1: V4, V8.

Statistical Data Analysis

The p-value for this regression model is given as 0.00 which is less than given level of significance or alpha value so we reject the null hypothesis that binary logistic regression model is not significant. We conclude that the binary logistic regression model is useful for the prediction of dependent variable child qualities: feeling of responsibility.

The binary logistic regression equation is given as below:

V14 = -0.518 + 0.154*V4 – 0.022*V8

By using this regression equation, we can predict the values for V14 or dependent variable child qualities: feeling of responsibility.

Discussion and Conclusions

From above statistical data analysis by using both parametric and non-parametric correlation coefficients, it is observed that there is insufficient evidence to conclude that there is a statistically significant relationship exists between the two variable family important and child qualities: feeling of responsibility. Also, it is observed that there is insufficient evidence to conclude that there is a statistically significant relationship exists between the two variable work important and child qualities: feeling of responsibility. This means, there is no any statistically significant relationship exists between the given dependent and independent variables. So, we cannot use the linear regression model for the prediction of the dependent variable child qualities: feeling of responsibility. We conclude that the binary logistic regression model is useful for the prediction of dependent variable child qualities: feeling of responsibility. These variables are not statistically related to each other and hence we cannot develop linear model for the prediction of dependent variable. From this study, two main conclusions as discuss above are summarised as below:

1. There is insufficient evidence to conclude that there is a statistically significant relationship exists between the two variable family important and child qualities: feeling of responsibility.
2. There is insufficient evidence to conclude that there is a statistically significant relationship exists between the two variable work important and child qualities: feeling of responsibility.
3. We conclude that the binary logistic regression model is useful for the prediction of dependent variable child qualities: feeling of responsibility.

References

Casella, G. and Berger, R. L. (2002). Statistical Inference. Duxbury Press.

Cox, D. R. and Hinkley, D. V. (2000). Theoretical Statistics. Chapman and Hall Ltd.

Degroot, M. and Schervish, M. (2002). Probability and Statistics. Addison – Wesley.

Dobson, A. J. (2001). An introduction to generalized linear models. Chapman and Hall Ltd.

Evans, M. (2004). Probability and Statistics: The Science of Uncertainty. Freeman and Company.

Hastle, T., Tibshirani, R. and Friedman, J. H. (2001). The elements of statistical learning: data mining, inference, and prediction: with 200 full-color illustrations. Springer – Verlag Inc.

Hogg, R., Craig, A., and McKean, J. (2004).  An Introduction to Mathematical Statistics. Prentice Hall.

Liese, F. and Miescke, K. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer.

Pearl, J. (2000). Casuality: models, reasoning, and inference. Cambridge University Press.

Ross, S. (2014). Introduction to Probability and Statistics for Engineers and Scientists. London: Academic Press.