Application of Multiple Regression Discussion Paper

The purpose of this assignment is to apply your understanding of simple and multiple linear regression.
For this assignment, use the \”Example Dataset\” to complete a simple linear regression using SPSS. Select one dependent variable, one primary independent variable, and one potential confounding variable. You will need to recode string variables into numeric variables to use them in the regression analysis. Prepare a Word document that includes all SPSS outputs.
Based on the results, create a second Word document and answer the following questions in 500-750 words.
State your research question and hypotheses.
Run the regression again without the potential confounding variable and discuss the impact on the coefficient of the primary independent variable. Did it change? If so, to what extent did it change? Based on this, do you think the added variable confounds the association between the independent and dependent variables?
Export both regression output tables as part of the Word document containing the SPSS outputs.  Application of Multiple Regression Discussion Paper
Provide your regression equation based on the results of the full regression model.
Interpret the results by (a) stating the reason the study or test was done; (b) presenting the main results, including coefficients on the main independent variable and significance levels; (c) explaining what the results mean; and (d) making suggestions for future research.
Submit both Word documents to the instructor.
APA style is not required, but solid academic writing is expected.
This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.
You are required to submit this assignment to LopesWrite. Refer to the LopesWrite Technical Support articles for assistance. please read the instruction very well

Application of multiple regression

The data was collected from a community with the intention of learning about the general health behaviors in the community as well as the relationship between health behaviors and environmental and social determinants. The present statistical analysis conducted on the collected data seeks to determine whether there is a relationship between a community member’s annual income and minutes exercised in a week. As such, the individual’s ‘annual income’ is the independent variable and the ‘minutes exercised in a weeks’ is the dependent variable. The simple linear regression analysis uses this information to determine expected minutes exercised in a week among community members whose annual income is known.

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Part 1. Three variables

For the linear regression analysis, three variables have been identified as: ‘minutes exercised in a week’ to act as the dependent variable, ‘annual income’ to act as the independent variable, and ‘age’ to act as a potential confounding variable. In this case, the analysis tries to predict minutes exercised in a week from the independent and confounding variables. As such, minutes exercised in a week (dependent variable) is the criterion, while annual income and age are the predictors (independent variables).

Application of Multiple Regression Discussion Paper

Based on the regression analysis, minutes exercised in a week can be predicted by computing:

Minutes exercised in a week = 42.069 + (0.001 * annual income) + (-0.013 * age)

The beta coefficient calculated for annual income is statistically significant (b=0.001, p=0.005). However, the beta coefficient calculated for age (b=-0.013, p=0.982) is not statistically significant. Still, the regression model is statistically significant in predicting the outcome variable and is a good fit for the data (p=0.018).

The R value has been calculated as 0.507, a high correlation showing that the model is not very precise in predicting minutes of exercise in a week. The R squared value of 0.257 shows that only 25.7% of the total variation in minutes exercised in a week (dependent variable) can be explained. The adjusted R square is presented as 0.201, a low figure that shows that the model does not do a good job for predicting minutes exercised in a week for the whole population (Montgomery, Peck & Vining, 2013).

Part 2. Two variables

For the linear regression analysis, two variables have been identified as: ‘minutes exercised in a week’ to act as the dependent variable, and ‘annual income’ to act as the independent variable. In this case, the analysis tries to predict minutes exercised in a week from the independent variable. As such, minutes exercised in a week (dependent variable) is the criterion, while annual income is the predictor (independent variable).

Based on the regression analysis, minutes exercised in a week can be predicted by computing:

Minutes exercised in a week = 41.586 + (0.001 * annual income)

The beta coefficient calculated for annual income is statistically significant (b=0.001, p=0.004).  Also, the regression model is statistically significant in predicting the outcome variable and is a good fit for the data (p=0.004).

The R value has been calculated as 0.507, a high correlation showing that the model is not very precise in predicting minutes of exercise in a week. The R squared value of 0.257 shows that only 25.7% of the total variation in minutes exercised in a week (dependent variable) can be explained. The adjusted R square is presented as 0.230, a low figure that shows that the model does not do a good job for predicting minutes exercised in a week for the whole population (Montgomery, Peck & Vining, 2013).

Part 3.

The added variable confounds the association between the independent and dependent variables. It has an effect on the result, and omitting it biases the coefficient estimated. Future research should control for the confounding variable by ensuring that all participants are of the same age so that any model determined would not be subject to omitted variable bias (Darlington & Hayes, 2017).

References

Darlington, R. B., & Hayes, A. F. (2017). Regression analysis and linear models: concepts, applications, and implementation. New York, NY: The Guilford Press.

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2013). Introduction to linear regression (5^th ed.). Hoboken, NJ: John Wiley & Sons, Inc.  Application of Multiple Regression Discussion Paper