# Research Paper On Regression

*Shalabh*

**shalab@iitk.ac.in**

**shalabh1@yahoo.com**

Department of Mathematics & Statistics

Indian of , - 208016 ()

Department of Mathematics & Statistics

Indian of , - 208016 ()

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*Research Papers *

1. Srivastava, A.K. and Shalabh (1995): "Predictions in Linear Regression Models With Measurement Errors", *Indian Journal of Applied Economics,* Vol. 4, No. 2, pp. 1-14.

2. Shalabh (1995): "Performance of Stein - rule Procedure for Simultaneous Prediction of Actual and Average Values of Study Variable in Linear Regression Model", *Bulletin of the International Statistical Institute, The ,* pp. 1375-1390.

3. Rao, B. and Shalabh (1995): "Unit Roots, Cointegration and the Demand for Money in ", *Applied Economic Letters*, 2, 397-399.

4. Srivastava, A.K. and Shalabh (1996): "Properties of a Consistent Estimation Procedure in Ultrastructural Model when Reliability Ratio is Known", *Microelectronics and Reliability*, Vol. 36, No. 9, pp. 1249-1252.

5. Srivastava, A.K. and Shalabh (1996): "Efficiency Properties of Least Squares and Stein-Rule Predictions in Linear Regression Model", *Journal of Applied Statistical Science*, Vol. 4, No. 2/3, pp. 141-145.

6. Srivastava, A.K. and Shalabh (1996): "A Composite Target Function for Prediction in Economic Models", *Indian Journal of Applied Economics,* Vol. 5, No. 5, pp. 251-257.

7. Toutenburg, H. and Shalabh (1996): "Predictive Performance of the Methods of Restricted and Mixed Regression Estimators", *Biometrical Journal,* 38, 8, pp. 951-959.

8. Srivastava, A.K. and Shalabh (1997): "A New Property of Stein Procedure in Measurement Error Model", *Statistics and Probability Letters,* 32, pp. 231-234.

9. Shalabh (1997): "Ratio Method of Estimation in the Presence of Measurement Errors", *Indian Journal of Agricultural Statistics,* Vol. 50, No.2, pp. 150-155.

10. Srivastava, A.K. and Shalabh (1997): "Improved Estimation of Slope Parameter in a Linear Ultrastructural Model when Measurement Errors are not Necessarily Normal", *Journal of Econometrics,* 78, pp. 153-157.

11. Shalabh (1997): "On Efficient Forecasting in Linear Regression Models", *Journal of Quantitative Economics*, Vol. 36, No. 2, pp. 133-140.

12. Srivastava, A.K. and Shalabh (1997): "Consistent Estimation for the Non-normal Ultrastructural Model", *Statistics and Probability Letters,* 34, pp. 67-73.

13. Srivastava, A.K. and Shalabh (1997): "Asymptotic Efficiency Properties of Least Squares Estimation in Ultrastructural Model", *TEST*, Vol. 6, No. 2, pp. 419-431.

14. Shalabh (1998): "Unbiased Prediction in Linear Regression Model with Equicorrelated Responses", *Statistical Papers*, Vol. 39, No. 2, pp.237-244.

15. Shalabh (1998): "Improved Estimation in Measurement Error Models Through Stein-rule Procedure", *Journal of Multivariate Analysis,* 67, 35-48. , Corrigendum : *Journal of Multivariate Analysis,* 74, p. 162, (2000).

16. Toutenburg, H. and Shalabh (1998) : "Prediction of Response Values in Linear Regression Models from Replicated Experiments", *SFB Discussion Paper 112*, of , .

17. Toutenburg, H. and Shalabh (1998) : "Use of minimum risk approach in the estimation of regression models with missing observation", *SFB Discussion Paper 118*, of , .

18. Toutenburg, H. and Shalabh (1998) : "Improved Predictions in Linear Regression Models with Stochastic Linear Constraints", *SFB Discussion Paper 124*, of , .

19. Shalabh (1999): "Improving the Predictions in Linear Regression Models", *Journal of Statistical Research*, Vol. 33, No. 1.

20. Toutenburg, H. and Shalabh (1999) : "Improving the Estimation of Incomplete Regression Models through Pilot Investigations and Repeated Studies", *SFB Discussion Paper 154*, of , .

21. Toutenburg, H. and Shalabh (1999) : "Estimation of Regression Coefficients Subject to Exact Linear Restrictions when some Observations are Missing and Balanced Loss Function is Used", *SFB Discussion Paper 163*, of , .

22. Toutenburg, H. and Shalabh (1999) : "Estimation of Regression Models with Equi-correlated Responses when some Observations on the Response Variable are Missing", *SFB Discussion Paper 174*, of , .

23. Toutenburg, H. and Shalabh (2000): "Improved Prediction in Linear Regression Model with Stochastic Linear Constraints", *Biometrical Journal,* 42, 1, 71-86.

24. Shalabh (2000): "Prediction of Values of Variables in Linear Measurement Error Model", *Journal of Applied Statistics*, 27, 4, 475-482.

25. Shalabh (2000): "Note on a Family of Unbiased Predictors for the Equi-correlated Responses in Linear Regression Models", *Statistical Papers*, Vol. 41, 2, pp. 237-241.

26. Shalabh and A.T.K. Wan (2000) : "Stein-rule Estimation in Mixed Regression Models", *Biometrical Journal ,* Vol 42, pp.203-214.

27. Srivastava A.K. and Shalabh (2000) : "On the Choice of Direction for Minimization of Residuals in Ultrastructural Model", *Statistica*, annoLX, n.1, 97-107.

28. Toutenburg, H. and Shalabh (2001) : "Use of Minimum Risk Approach in the Estimation of Regression Models with Missing Observations", *Metrika*, 54, 247-249.

29. Shalabh (2001): "Consistent Estimation through Weighted Harmonic Mean of Inconsistent Estimators in Replicated Measurement Error Models", *Econometric Reviews, *Vol. 20, 4, 507-510.

30. Toutenburg, H. and Shalabh (2001) : "A note on the comparison of minimax linear and mixed regression estimation of regression coefficients when prior estimates are available", *SFB Discussion Paper* 238, of , .

31. Toutenburg, H. and Shalabh (2001) : "Estimation of Linear Models with Missing Data: The role of Stochastic Linear Constraints", *SFB Discussion Paper* 239, of , .

32. Ullah, A., Shalabh and D. Mukherjee (2001): "Consistent Estimation of Regression Coefficients in Replicated data with non-normal Measurement Errors", *Annals of Economics and Finance*, 2, 249-264.

33. Toutenburg, H. and Shalabh (2001): "Use of Prior Information in the form of interval constraints for the Improved Estimation of Linear Regression Models with some Missing Responses", *SFB Discussion Paper *240, of , .

34. Srivastava, A.,K. and Shalabh (2001): "Effect of Measurement Errors On the Regression Method of Estimation in Survey Sampling", *Journal of Statistical Research*, Vol. 35, No. 2 , pp. 35-44.

35. Shalabh (2001) : "Estimation of Bias and Standard Error of An Improved Estimator of Mean", *Metrika*, 54, 43-51.

36. Toutenburg, H. and Shalabh (2001) : "Synthesizing the Classical and Inverse Methods in Linear Calibration", *SFB Discussion Paper* 252, of , .

37. Shalabh (2001): "Least Squares Estimators in Measurement Error Model under the Balanced Loss Function", *TEST,* Vol. 10, 2, 301-308.

38. Shalabh (2001) : "Pitman Closeness Comparison of Least Squares and Stein-rule Estimators in Linear Regression Models with Non-normal Disturbances", *The American Journal of Mathematical and Management Sciences (AJMMS),* Vol. 21, No. 1 , pp. 89-100.

39. Shalabh (2002) : "Effects of a Trended Regressor on the Efficiency Properties of the Least Squares and Stein-rule Estimation of Regression Coefficients", *Handbook of Applied Econometrics and Statistical Inference,* Editors: A. Ullah, A. Wan and A. Chaturvedi, Marcell Dekker, pp. 327-346.

40. Toutenburg, H. and Shalabh (2002) : "Prediction of Response Values in Linear Regression Models from Replicated Experiments", *Statistical Papers,* 43, pp. 423-433.

41. Shalabh and R. Chandra (2002): "Prediction in Restricted Regression Models", *Journal of Combinatorics, Information System and Sciences, *Vol. 29, Nos. 1-4, pp. 229-238.

42. Toutenburg, H. and Shalabh (2003) : "Pseudo Minimax Linear and Mixed Regression Estimation of Regression Coefficients when Prior Estimates are available", *Statistics and Probability Letters*, 63, pp. 35-39.

43. Toutenburg, H. and Shalabh (2003): "Estimation of Regression Models with Equi-correlated Responses when Some Observations on Response Variable are Missing", *Statistical Papers, *Vol. 44, No. 10, pp. 217-232.

44. Shalabh (2003): "Consistent Estimation of Coefficients in Measurement Error Models with Replicated Observations", *Journal of Multivariate Analysis*, Vol. 86, No. 2, pp. 227-241.

45. Schaffrin, B., H. Toutenburg and Shalabh (2003): "On the Impact of Missing Values on the Reliability Measures in a Linear Model", Journal of Statistical Research, (Invited paper for Special Volume in Honor of Professor A.K.Md.E. Saleh) , 37, 2, pp. 251-260.

46. Chaturvedi, A. and Shalabh (2004): "Risk and Pitman Closeness Properties of Feasible Generalized Double k-class estimators in Linear Regression Models with Non-spherical Disturbances under Balanced Loss Function", *Journal of Multivariate Analysis*, 90, 229-256.

47. J. Gleser and Ori Rosen (2004): "On the Usefulness of Knowledge of Error Variances in the Consistent Estimation of an Unreplicated Ultrastructural Model", *Journal of Statistical Computation & Simulation,* 74, 6, pp. 391-417.

48. Shalabh and H. Toutenburg (2005): "Consequences of Departure from Normality on the Properties of Calibration Estimators", Discussion paper 441, of , .

49. Shalabh and H. Toutenburg (2005): "On the regression method of estimation of population mean from incomplete survey data through imputation", Discussion paper 442, of , .

50. Toutenburg, H. and Shalabh (2005): "Estimation of Linear Models with Missing Data: The Role of Stochastic Linear Constraints", *Communications in Statistics - Theory and Methods* Volume 34, 2, pp. 375-387.

51. Toutenburg, H. and Shalabh (2005): "Estimation of Regression Coefficients subject to Exact Linear Restrictions when some observations are missing and Balanced Loss Function is used", *TEST*, Vol. 14, No. 2, pp. 385-396.

52. Toutenburg, H., V.K. Srivastava, Shalabh and C. Heumann (2005): "Estimation of Parameters in Multiple Regression With Missing Covariates using a Modified First Order Regression Procedure", *Annals of Economics and Finance*, 6, pp. 289-301.

53. H. Schneeweiss and Shalabh (2006): " On the Estimation of the Linear Relation when the Error Variances are known", Discussion paper 493, of , .

54. Shalabh, H. Toutenburg and C. Heumann (2006): "Risk Performance Of Stein-Rule Estimators Over The Least Squares Estimators Of Regression Coefficients Under Quadratic Loss Structures", Discussion paper 495, of , .

55. Shalabh, H. Toutenburg and C. Heumann (2006): " Mean squared error matrix comparison of least squares and Stein-rule estimators for regression coefficients under non-normal disturbances", Discussion paper 496, of , .

56. Shalabh, H. Toutenburg and C. Heumann (2006): " Performance of Double *k*-class Estimators for Coefficients in Linear Regression Models with Non Spherical Disturbances under Asymmetric Losses", Discussion paper 509, of , .

57. Toutenburg, H., V.K. Srivastava and Shalabh (2006): "Estimation of Linear regression Models with Missingness of Observations on Both the Explanatory and Study Variables", *Quality Technology and Quality Management, *Vol. 3, No. 2*, *pp. 179-189.

58. Toutenburg, H., Shalabh and C. Heumann (2006) : "Use of Prior Information in the Form of Interval Constraints for Improved Estimation of Linear Regression Models with Some Missing Responses", *Journal of Statistical Planning and Inference,* Vol. 136, No. 8, pp. 2430-2445.

59. Shalabh and H. Toutenburg (2006): "Consequence of Departure from Normality on the Properties of Calibration Estimators", *Journal of Statistical Planning and Inference*, Vol. 136, No. 12, pp. 4385-4396.

60. A. Kukush, A. Malenko, H. Schneeweiss and Shalabh (2007): "Optimality of Quasi-Score in the Multivariate Mean-Variance Model with an Application to the Zero-Inflated Poisson Model with Measurement Errors", Discussion paper 498, of , .

61. Shalabh and Pen-Hwang Liau (2007): "Consistent Estimation of Regression Coefficient Through Weighted Arithmetic Mean of Inconsistent Estimators in Replicated Ultrastructural Model", *Communications in Statistics**(Theory and Methods)*, Volume 36, Issue 5, pp. 955-960.

62. C. Heumann and Shalabh (2007): "Weighted Mixed Regression Estimation Under Biased Stochastic Restrictions", Technical Report No. 10, Department of Statistics, of , .

63. M. Wissmann, H. Toutenburg and Shalabh (2007): "Role of Categorical Variables in Multicollinearity in Linear Regression Model", Technical Report No. 8, Department of Statistics, of , .

64. Shalabh, H. Toutenburg and C. Heumann (2007): "Stein-Rule Estimation under an Extended Balanced Loss Function", Technical Report No. 7, Department of Statistics, of , .

65. H. Schneeweiss and Shalabh (2007): "On the Estimation of the Linear Relation when the Error Variances are known", *Computational Statistics and Data Analysis*, Vol. 52, pp. 1143 -1148.

66. Shalabh, Gaurav Garg and Neeraj Misra (2007): "Restricted Regression Estimation in Measurement Error Models", *Computational Statistics and Data Analysis *52*, *pp. 1149 -1166.

67. Singh, H.P. and Shalabh (2007): "Estimation of population mean through estimated coefficient of variation", *Journal of Applied Statistical Science, *Volume 15, Issue 4, pp. 425-429.

68. Shalabh, H. Toutenburg and C. Heumann (2007): "Risk Performance of Stein-Rule Estimators over the Least Squares Estimators of Regression Coefficients under Quadratic Loss Structures", * Journal of Statistical Studies *( *Invited paper for the special issue in honor of *75*th birthday of Professor A.K.Md.E. Saleh*)Vol. 26, pp. 97-103.

69. Shalabh and Alan Wan (2007): ``A Class of Estimators of Regression Coefficient for Sign Change Problem in Measurement Error Models'', * Journal of Statistical Research,* Vol. 41, No. 2, pp. 63-72.

70. Toutenburg, H. and Shalabh (2008): "Improving the Estimation of Incomplete Regression Models through Pilot Investigations and Repeated Studies", *Journal of Applied Statistical Science, *Volume 16, No. 1, pp. 127-145.

71. Shalabh, C.M. Paudel and (2008): "Simultaneous Prediction of Actual and Average Values of Response Variable in Replicated Measurement Error Models " in * Recent Advances In Linear Models and Related Areas *(Springer) (Editors: Shalabh and C. Heumann), pp. 105-133.

72. Toutenburg, H., V.K. Srivastava and Shalabh (2008): "Amputation versus imputation of missing values through ratio method in sample surveys", *Statistical Papers, *Vol. 49, No. 2, pp. 237-247.

73. C. Heumann and Shalabh (2008): "Weighted Mixed Regression Estimation Under Biased Stochastic Restrictions" in * Recent Advances In Linear Models and Related Areas *(Springer) (Editors: Shalabh and C. Heumann), pp. 401-416.

74. Gaurav Garg and Shalabh (2008): "Stein-rule Estimation in Ultrastructural Model Under Exact Linear Restrictions", *Journal of Statistical Research ( Invited paper for the special issue in honor of Professor Mir Maswood Ali) *Vol. 42, No. 2, pp. 159-180.

75. Shalabh, H. Toutenburg and C. Heumann (2008): "Mean Squared Error Matrix comparison of Least Squares and Stein-Rule Estimators for Regression Coefficients under Non-normal Disturbances", *Metron, *Vol. LXVI, No. 3, pp. 285-298.

76. H. Toutenburg, Shalabh and C. Heumann (2009): "Optimal Estimation in a Linear Regression Model Using Incomplete Prior Information'' in ** Statistical Inference, Econometric Analysis and Matrix Algebra**(Springer) (Editors: Bernhard Schipp and Walter Kraemer), pp. 185-200.

77. Pen-Hwang Liau and Shalabh (2009): "Confidence Interval Estimation in Ultrastructural Model", *Communications in Statistics**(Theory & Methods)*, 38:5, pp. 675-681.

78. Shalabh, C.M. Paudel and N. Kumar (2009): "Consistent estimation of regression parameter under replicated ultrastructural model with non-normal errors", * Journal of Statistical Computation & Simulation*, Vol. 79, No. 3, pp. 251-274.

79. Shalabh, Gaurav Garg and Neeraj Misra (2009): "Use of Prior Information in the Consistent Estimation of Regression Coefficients in a Measurement Error Model", *Journal of Multivariate Analysis*, Vol. 100, pp. 1498-1520.

80. Shalabh, H. Toutenburg and C. Heumann (2009): "Stein-Rule Estimation under an Extended Balanced Loss Function", *Journal of Statistical Computation & Simulation*, Vol. 79, No. 10, pp. 1259-1273.

81. A. Kukush, A. Malenko, H. Schneeweiss and Shalabh (2010): "Optimality of Quasi-Score in the Multivariate Mean-Variance Model with an Application to the Zero-Inflated Poisson Model with Measurement Errors", *Statistics*, Vol. 44, No. 4, pp. 381-396.

82. Shalabh, Gaurav Garg and Neeraj Misra (2010): "Consistent Estimation of Regression Coefficients in Measurement Error Model Using Stochastic Apriori Information", *Statistical Papers*, Vol. 51, pp.717-748.

83. Shalabh, H. Toutenburg and A. Fieger (2010): "Using Diagnostic Measures to Detect Non-MCAR Processes in Linear Regression Models With Missing Covariates" *Journal of Statistical Research*, Vol. 44, No. 2, pp. 233-242 (Invited paper in honor of Professor Bradley Efron).

84. Shalabh and C. Heumann (2011): "Simultaneous Prediction of Actual and Average Values of Study Variable Using Stein-rule Estimators", Technical Report No. 104, Department of Statistics, University of Munich, Munich, Germany.

85. Shalabh, Gaurav Garg and Neeraj Misra (2011): Estimation of Regression Coefficients in a Restricted Measurement Error Model using Instrumental Variables", *Communications in Statistics (Theory & Methods), *Vol. 40, pp. 3614-3629.

86. Gaurav Garg and Shalabh (2011): "Simultaneous Predictions under Exact Restrictions in Ultrastructural Model'', *Journal of Statistical Research* (in Special Volume on Measurement Error Models) Vol. 45, No. 2, pp. 139-154.

87. M. Wissmann, H. Toutenburg and Shalabh (2011): "Role of Categorical Variables in Multicollinearity in Linear Regression Model", *Journal of Applied Statistical Science, *Volume 19, Issue 1, pp. 99-113.

88. Karthikeyan, G., J. Ramkumar and Shalabh (2012): "Performance Analysis of mu-ED-Milling Process Using Various Statistical Techniques'', *International Journal of Machining and Machinability of Materials,* 123, pp. 183-203.

89. Shalabh and C. Heumann (2012): "Simultaneous Prediction of Actual and Average Values of Study variable Using Stein-rule Estimators" in *Some Recent Developments in Statistical Theory and Application*, (Editors: K. Kumar and A. Chaturvedi), pp. 68-81, Brown Walker Press, U.S.A.

90. Sangita Kulathinal, Shalabh and Bijoy Joseph (2012): "Analysis of Pooled Time Series and Spatial Data with an Application to Water Level Data'', *Journal of Applied Statistical Science, *Vol. 18, No. 3, pp. 419-430.

91. Shalabh, G. Garg and C. Heumann (2012): "Performance of Double k-class Estimators for Coefficients in Linear Regression Models with Non Spherical Disturbances under Asymmetric Losses'', *Journal of Multivariate Analysis*, 112, pp. 35-47.

92. Shalabh (2013): "A revisit to the efficient forecasting in linear regression models'', *Journal of Multivariate Analysis*, 114, pp. 161-169.

93. A.K.Md.E. Saleh and Shalabh (2014): "Ridge Regression Estimation Approach to Measurement Error Model", *Journal of Multivariate Analysis, *123, pp. 68-84. Extended version of the paper [*This paper is in the category of ``Most Downloaded paper'' from JMVA in January 2014*]

Corrigendum: *Journal of Multivariate Analysis, *2014, 127, pp. 214.

94. C.L. Cheng, Shalabh and G. Garg (2014): "Coefficient of Determination for Multiple Measurement Error Models", *Journal of Multivariate Analysis, * 123, pp. 137-152. [*This paper is in the category of ``Most Downloaded paper'' from JMVA in January 2014*.]

95. Anoop Chaturvedi and Shalabh (2014): "Bayesian Estimation of Regression Coefficients under Extended Balanced Loss Function", * Communications in Statistics - Theory and Methods*, Vol. 43, pp. 4253-4264.

96. C.L. Cheng, Shalabh and G. Garg (2016) : "Goodness of Fit in Restricted Measurement Error Models", *Journal of Multivariate Analysis, *145, pp. 101-116.

97. Shalabh and C. Heumann (2017): "Use of Regression Method for Estimating Population Mean from Incomplete Survey Data through Imputation", *Journal of Applied Statistical Science*, Vol. 22, No. 3-4, pp. 407-427.

98. Shalabh and Jia-Ren Tsai (2017): "Ratio and Product Methods of Estimation of Population Mean in the Presence of Correlated Measurement Errors'', * Communications in Statistics (Simulation and Computation), *Vol. 46, No. 7, pp. 5566-5593.

99. Shalabh, Jia-Ren Tsai and Pen-Hwang Liau (2016): "Immaculating the Inconsistent Estimator of Slope Parameter in Measurement Error Model with Replicated Data", *Journal of Statistical Computation and Simulation*, (In press).

1. G. Karthikeyan, J. Ramkumar and Shalabh (2009): ``Estimation of Diameter Machining of Tungsten Electrode by Micro Block EDG Process'', Proceedings of IPRoMM 2009 (National Conference on Design and Manufacturing Issues in Automotive and Allied Industries), 10-11 July 2009, Chennai, India, Eds. R. Gnanamoorthy, M. Kamraj and M. Sreekumar.

2. Shalabh and G. Garg (2013): ``Coefficient of Determination for Multiple Measurement Error Models'', Proceedings of the 59th ISI (International Statistical Institute) World Statistics Congress, 25-30 August 2013, Hong Kong (Session STS044).

*Data analysis using multiple regression analysis is a fairly common tool used in statistics. Many people find this too complicated to understand. In reality, however, this is not that difficult to do especially with the use of computers. *

How is multiple regression analysis done? This article explains this very useful statistical test when dealing with multiple variables then provides an example to demonstrate how it works.

Multiple regression analysis is a powerful statistical test used in finding the relationship between a given dependent variable and a set of independent variables. The use of multiple regression analysis requires a dedicated statistical software like the popular Statistical Package for the Social Sciences (SPSS), Statistica, Microstat, among other sophisticated statistical packages. It will be near impossible to do the calculations manually.

However, a common spreadsheet application like Microsoft Excel can help you compute and model the relationship between the dependent variable and a set of predictor or independent variables. But you cannot do this without activating first the set of statistical tools that ship with MS Excel. To activate the add-in for multiple regression analysis in MS Excel, view the Youtube tutorial below.

### Example of a Research Using Multiple Regression Analysis

I will illustrate the use of multiple regression by citing the actual research activity that my graduate students undertook two years ago. The study pertains to the identification of the factors predicting a current problem among high school students, that is, the long hours they spend online for a variety of reasons. The purpose is to address the concern of many parents on their difficulty of weaning their children away from the lures of online gaming, social networking, and other interesting virtual activities.

Upon reviewing the literature, the graduate students discovered that there were very few studies conducted on the subject matter. Studies on problems associated with internet use are still in its infancy.

The brief study using multiple regression is a broad study or analysis of the reasons or underlying factors that significantly relate to the number of hours devoted by high school students in using the Internet. The regression analysis is broad in the sense that it only focuses on the total number of hours devoted by high school students to activities online. The time they spent online was correlated with their personal profile. The students’ profile consisted of more than two independent variables; hence the term “multiple”. The independent variables are age, gender, relationship with the mother, and relationship with the father.

The statement of the problem in this study is:

“Is there a significant relationship between the total number of hours spent online and the students’ age, gender, relationship with their mother, and relationship with their father?”

The relationship with their parents was gauged using a scale of 1 to 10; 1 being a poor relationship, and 10 being the best experience with parents. The figure below shows the paradigm of the study.

Notice that in multiple regression studies such as this, there is only one dependent variable involved. That is the total number of hours spent by high school students online. Although many studies have identified factors that influence the use of the internet, it is standard practice to include the profile of the respondents among the set of predictor or independent variables.

Hence, the common variables age and gender are included in the multiple regression analysis. Also, among the set of variables that may influence internet use, only the relationship between children and their parents were tested. The intention is to find out if parents spend quality time to establish strong emotional bonds between them and their children.

### Findings of the Study

What are the findings of this exploratory study? The multiple regression analysis revealed an interesting finding.

The number of hours spent online relates significantly to the number of hours spent by a parent, specifically the mother, with her child. These two factors are inversely or negatively correlated. The relationship means that the greater the number of hours spent by the mother with her child to establish a closer emotional bond, the lesser the number of hours spent by her child in using the internet. The number of hours spent online relates significantly to the number of hours spent by the mother with her child

The number of hours spent online relates significantly to the number of hours spent by the mother with her child

While this may be a significant finding, the mother-child bond accounts for only a small percentage of the variance in total hours spent by the child online. This observation means that there are other factors that need to be addressed to resolve the problem of long waking hours and abandonment of serious study of lessons by children. But establishing a close bond between mother and child is a good start.

### Conclusion

The above example of multiple regression analysis demonstrates that the statistical tool is useful in predicting the behavior of dependent variables. In the above case, this is the number of hours spent by students online.

The identification of significant predictors can help determine the correct intervention resolve the problem. The use of multiple regression approaches prevents unnecessary costs for remedies that do not address an issue or a problem.

Thus, in general, research employing multiple regression analysis streamlines solutions and brings into focus those influential factors that must be given attention.

©2012 November 11 Patrick Regoniel

Cite this article as: Regoniel, Patrick A. (November 11, 2012). Example of a Research Using Multiple Regression Analysis. In *SimplyEducate.Me*. Retrieved from http://simplyeducate.me/2012/11/11/example-of-a-research-using-multiple-regression-analysis/

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