Curvilinear Regression (Cubic)

sagar gaikwad

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May 17, 2021, 9:20:18 PM5/17/21

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Respected Neeraj Sir and Group Members,

In the curvilinear regression how to interpret the result of cubic curve relationship. The value of Durbin Watson is not generated, and the coefficients are found to be insignificant, how to make a regression model in such cases.

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

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Neeraj Kaushik

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May 18, 2021, 3:52:39 AM5/18/21

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Dear Sagar

Plz aware of why you are using the Curvilinear regression?

Best wishes

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sagar gaikwad

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May 18, 2021, 4:03:36 AM5/18/21

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Respected sir,

I am using curvilinear because curve estimation suggests that linear is having low R Square value and Cubic is having good R Square value.

Model Summary and Parameter Estimates
Dependent Variable: Work_Engagement
Equation	Model Summary					Parameter Estimates
Equation	R Square	F	df1	df2	Sig.	Constant	b1	b2	b3
Linear	.103	102.705	1	898	.000	99.169	-.606
Logarithmic	.111	111.670	1	898	.000	125.649	-13.210
Inverse	.109	110.398	1	898	.000	72.801	248.418
Quadratic	.120	60.898	2	897	.000	116.495	-2.356	.038
Cubic	.124	42.292	3	896	.000	87.741	1.970	-.163	.003
Compound	.099	98.458	1	898	.000	101.937	.991
Power	.106	106.045	1	898	.000	150.329	-.194
S	.104	104.241	1	898	.000	4.237	3.641
Growth	.099	98.458	1	898	.000	4.624	-.009
Exponential	.099	98.458	1	898	.000	101.937	-.009
The independent variable is Tunover_Intention.

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

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Neeraj Kaushik

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May 18, 2021, 4:05:02 AM5/18/21

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Plz re-run the model by opting not to take construct in the model

If the IDV is still not significant then use Linear regression.

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sagar gaikwad

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May 18, 2021, 4:34:53 AM5/18/21

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Respected sir,

Great input sir,

By not opting constant in the model, IDV are found to be significant in curvilinear cubic. Can this model without constants be a good model.

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

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Neeraj Kaushik

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May 18, 2021, 4:38:43 AM5/18/21

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A Quadratic model seems a better solution here.

Model without Intercept indicates that when x=0, y=0

It means that the regression line is passing through the origin.

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sagar gaikwad

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May 18, 2021, 4:47:37 AM5/18/21

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Respected sir,

Thank you so much. Many doubts are cleared today. Thank you again.

Good day sir.

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

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Dr. Nisha Arora

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May 25, 2021, 12:12:50 AM5/25/21

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Hi Sagar,
I would like to add something to the discussion.
1. Seems like you have just one predictor (case of simple regression). Scatter plot will give you insight into the type of relationship. Always start the analysis by exploring and understanding your data. And also see what does the theory says about your variables?

2. Did you check for model assumptions? Is RSE 20 acceptable? which model evaluation matric you need? [This question usually scholars ignore as they always refer to R sq and Adj R sq, maybe you can leave it too]
Always perform post estimation analysis _ Using plots and/or tests. [R is great for these but we can very well do this in SPSS too]
And make changes if required.

3. To compare different models, R has great functionalities [anova() function and many more. See the screenshot below. Or you may find some reference code on my GitHub page]
Maybe you can do this manually in SPSS.

4. Removing intercept has its own consequences, keep in mind those.

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Dr. Nisha Arora

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r code_compare models.png

r output_model performance.png

sagar gaikwad

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May 25, 2021, 3:11:21 AM5/25/21

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Dear Dr. Nisha Madam

Thank you so much for your insights on my query.

1. I have performed curve estimative in SPSS to understand the relationship between two variables. I have used the model whose R is greater

2. I have checked R square and Adj R Square for the model suggested in curve estimation. Please guide how to check RMSE in SPSS for a regression model.

3. I have checked R when I have performed curve estimation in SPSS for all the types of relationship.

4. Agree madam, Skipping constant in the regression model is not a good option.

Please guide further if I am wrong in the above statements.

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

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Dr. Nisha Arora

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May 26, 2021, 2:17:37 AM5/26/21

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Hi Sagar,
Seems like you couldn't understand the points shared by me. However, you are correct in your observations, you can proceed as suggested by Neeraj Sir.
Theoretically, RSE (Residual standard error) is different from RMSE (Root Mean Square Error).
RSE (you get in output of lm() function in R directly) tells you how much your average response will deviate from the regression line or how far are your predictions?

SPSS uses 'Standard error of Estimate' to represent RMSE and hence the confusion.

Refer: https://www.ibm.com/support/pages/definition-standard-error-estimate-printed-linear-regression-model-summary

and Book: Introduction to Statistical Learning with R

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Sagar Gaikwad

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May 26, 2021, 3:53:34 AM5/26/21

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Respected Madam,

Thank you so much for the clarification. Just now I watched a video on how to calculate Standard error of Estimate in SPSS.

Thanks & Regards,

Mr. Sagar Gaikwad

Assistant Professor & Ph. D Coordinator

Vidyalankar School of Information Technology

Mob No: 9833376766

Online Profile: https://vsit.edu.in/faculty_sagar_gaikwad.html

ORCID ID : 0000-0002-3816-2801

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