Per the instruction on the exercise paper: ”

Please submit the **questions and answers only, no SPSS output.** You do not need a APA title or reference page. make sure to save your document with the correct title as directed in the submission area.

To clarify, we do not need to export the SPSS to any word document this week? We only submit the answers, correct? Please correct me if I am wrong.

In statistical analysis, linear regression refers to the linear approaches in modeling the relationship that exists between the scalar response and one or more explanatory variables. In the case of one explanatory variable, simple linear regression is always applicable. On the other hand, for more than one explanatory variable, multiple linear regression is often applied to enhance outcomes’ accuracy (Darlington & Hayes, 2017). In the regression analysis, the relationship between the dependent and independent variables is modeled through the application of linear predictor functions whose unidentified model parameters can be estimated from the data and information given; these models are called linear models.

One of the main strengths of linear regression it can be generalized to avoid overfitting. Also, the linear models can be easily updated in case there is new data through the application of stochastic gradient descent (Abdillah et al., 2020). Finally, linear regression applies a very simple algorithm to enhance the achievement of satisfactory outcomes; with the method, there is always low computational power in the determination of the desired outcomes or predictor variable.

The peer-reviewed article, “Association between body mass index and onset of hypertension in men and women with and without diabetes: a cross-sectional study using national health data from the State of Kuwait in the Arabian Peninsula.” by Channanath et al. (2015) applies regression analysis in the process of data analysis. The regression analysis was used in the article because there was a need to determine the relationship between the dependent and independent variables. In other words, there was the evaluation of the associations that exist between age and BMI at the onset of hypertension through the performance of multiple linear regression. The challenge in interpreting the result of the regression was associated with the outliers in the dataset.

**References**

Abdillah, A., Sutisna, A., Tarjiah, I., Fitria, D., & Widiyarto, T. (2020, March). Application of Multinomial Logistic Regression to analyze learning difficulties in statistics courses. In *Journal of Physics: Conference Series* (Vol. 1490, No. 1, p. 012012). IOP Publishing. Retrieved from: https://iopscience.iop.org/article/10.1088/1742-6596/1490/1/012012/meta

Channanath, A. M., Farran, B., Behbehani, K., & Thanaraj, T. A. (2015). Association between body mass index and onset of hypertension in men and women with and without diabetes: a cross-sectional study using national health data from the State of Kuwait in the Arabian Peninsula. *BMJ open*, *5*(6), e007043. Retrieved from: https://bmjopen.bmj.com/content/5/6/e007043.short

Darlington, R. B., & Hayes, A. F. (2017). Regression analysis and linear models. *New York, NY: Guilford*. Retrieved from: https://doc1.bibliothek.li/acd/FLMF052309.pdf

Simple Linear Regression

**What is the total sample size?**

The sample size is 378

**What is the mean income and mean number of hours worked? **

The mean for income and the number of hours worked are $1,485.49 and 33.52 respectively.

**What is the correlation coefficient between the outcome and predictor variables? Is it significant? How would you describe the strength and direction of the relationship?**

The correlation coefficient between the outcome and predictor variable is 0.3; this indicates a weak positive correlation.

**What it the value of R squared (coefficient of determination)? Interpret the value.**

The value of R squared is 0.088. This means that there is a weak effect size with only 8.8% of the data fitting in the model.

**Interpret the standard error of the estimate? What information does this value provide to the researcher? **

The standard error of the estimate is $907.877; this indicates a high level of variation in the regression model.

**The model fit is determined by the ANOVA table results (***F* statistic = 37.226, 1,376 degrees of freedom, and the *p* value is .001). Based on these results, does the model fit the data? Briefly explain. (Hint: A significant finding indicates good model fit.)

The model fit because the p-value is smaller than the critical alpha, p=0.05.

**Based on the coefficients, what is the value of the y-intercept (point at which the line of best fit crosses the y-axis)? **

The value of y-intercept is 711.651.

**Based on the output, write out the regression equation for predicting family income.**

The regression equation =Family income = 711.651 + 23.083 hours worked per week.

**Using the regression equation, what is the predicted monthly family income for women working 35 hours per week? **

The predicted monthly family income=711.651 + 23.083*35 = 1519.556

**Using the regression equation, what is the predicted monthly family income for women working 20 hours per week? **

The predicted monthly income for a working for 20 hours per week = 711.651+ 23.083* 20 =1,173.311.

**Part 2**

**Analyze the data from the SPSS output and write a paragraph summarizing the findings. (Use the example in the SPSS output file as a guide for your write-up.)**

The findings indicates that age, education attainment, currently employed and the number and types of abuse predict the CES-D scores. The correlation coefficient value was r=0.412. The model fits the relationship between the predictor and outcoem variables, F=31.506, sig.000.

**Which of the predictors were significant predictors in the model? **

The CES-D score was significantly correlated to the number and types of abuses (0.37).

**Which of the predictors was the most relevant predictor in the model? **

The number and types of abyuse was the more relevant predictor.

**Interpret the unstandardized coefficents for educational attainment and poor health.**

The unstandardized coefficient values indicate a strong correlation between the poor health self rating and the CES-D scores. The Beta value was 10.928.

**If you wanted to predict a woman’s current CES-D score based on the analysis, what would the unstandardized regression equation be? Include unstandardized coefficients in the equation. **

The unstandarized regression equation will be:

CES-D score = 18.165 + 0.068 respondents age at the time of interview – 2.518 educational attainment – 3.605 currently employed +9.496 poor health rating + 3.432 number and types pfabuses.

**Weekly Participation**

Your initial responses to the mandatory DQ do not count toward participation and are graded separately.

In addition to the DQ responses, you must post at least one reply to peers (or me) on three separate days, for a total of three replies.

Participation posts do not require a scholarly source/citation (unless you cite someone else’s work).

Part of your weekly participation includes viewing the weekly announcement and attesting to watching it in the comments. These announcements are made to ensure you understand everything that is due during the week.

**APA Format and Writing Quality**

Familiarize yourself with APA format and practice using it correctly. It is used for most writing assignments for your degree. Visit the Writing Center in the Student Success Center, under the Resources tab in LoudCloud for APA paper templates, citation examples, tips, etc. Points will be deducted for poor use of APA format or absence of APA format (if required).

Cite all sources of information! When in doubt, cite the source. Paraphrasing also requires a citation.

I highly recommend using the APA Publication Manual, 6th edition.

**Use of Direct Quotes**

I discourage overutilization of direct quotes in DQs and assignments at the Masters’ level and deduct points accordingly.

As Masters’ level students, it is important that you be able to critically analyze and interpret information from journal articles and other resources. Simply restating someone else’s words does not demonstrate an understanding of the content or critical analysis of the content.

It is best to paraphrase content and cite your source.

**LopesWrite Policy**

For assignments that need to be submitted to LopesWrite, please be sure you have received your report and Similarity Index (SI) percentage BEFORE you do a “final submit” to me.

Once you have received your report, please review it. This report will show you grammatical, punctuation, and spelling errors that can easily be fixed. Take the extra few minutes to review instead of getting counted off for these mistakes.

Review your similarities. Did you forget to cite something? Did you not paraphrase well enough? Is your paper made up of someone else’s thoughts more than your own?

Visit the Writing Center in the Student Success Center, under the Resources tab in LoudCloud for tips on improving your paper and SI score.

**Late Policy**

The university’s policy on late assignments is 10% penalty PER DAY LATE. This also applies to late DQ replies.

Please communicate with me if you anticipate having to submit an assignment late. I am happy to be flexible, with advance notice. We may be able to work out an extension based on extenuating circumstances.

If you do not communicate with me before submitting an assignment late, the GCU late policy will be in effect.

I do not accept assignments that are two or more weeks late unless we have worked out an extension.

As per policy, no assignments are accepted after the last day of class. Any assignment submitted after midnight on the last day of class will not be accepted for grading.

**Communication**

Communication is so very important. There are multiple ways to communicate with me:

Questions to Instructor Forum: This is a great place to ask course content or assignment questions. If you have a question, there is a good chance one of your peers does as well. This is a public forum for the class.

Individual Forum: This is a private forum to ask me questions or send me messages. This will be checked at least once every 24 hours.