Respond to these posts and comment on the following:

1. Do you think the variables are appropriately used? Why or why not?
2. Does the analysis answer the research question? Be sure and provide constructive and helpful comments for possible improvement.
3. If there was a significant effect, comment on the strength and its meaningfulness.
4. Asalayreader,wereyouabletounderstandtheresultsandtheirimplications?Whyorwhynot?

Post 1

"Good evening, Colleagues,

For this discussion, I was interested in exploring the relationship between two metric level variables. Bivariate correlation and regression analysis are useful ways of showing the relationship between two interval-ratio variables (Frankfort-Nachmias& Leon-Guerrero, 2015). In this discussion, I will propose a research question and null hypothesis surrounding the two variables, propose an appropriate research design, describe the variables used to calculate test statistics, and interpret the results, commenting on the strength of the effect. I will conclude with a brief explanation in laymans terms to further explain the answer to the research question.

Research Question and Null Hypothesis

For this discussion exercise, I chose two quantitative variables measured at the interval-ratio level from the Data Set 2014 General Social Survey (Data Set, 2014); the RESPONDENT INCOME IN CONSTANT DOLLARS (conrinc) variable and the HOURS PER DAY WATCHING TV (tvhours) variable. I propose the following research question: Is there a relationship between the number of hours spent watching television (TV) and a persons income (measured in constant dollars). An appropriate null hypothesis would read: There is no relationship between the number of hours spent watching TV and a persons annual income. Stated differently, I could hypothesize that the number of hours spent watching TV is not a predictor of a persons income.

Research Design

This research question explores the relationship between two metric level variables. Since manipulation of variables is not indicated, a non-experimental,correlational, quantitative research design is suggested (Grove, Burns, & Gray, 2013). In order to explore the relationship, a correlation coefficient is calculated. Described as one of the most commonly used statistical tools, correlation coefficients describe the association between variables (Magnusson, n.d.). Pearson correlation coefficients, a type of parametric measure, allow the researcher to determine the strength and direction (positive or negative) of the relationship between pairs and evaluate whether there is statistical evidence of a linear relationship between them (Kent State University [Kent State], 2014).

To determine the degree of the relationship, a bivariate regression analysis is indicated. The bivariate regression coefficient indicates to what degree there is a relationship by estimating the difference in the outcome (dependent) variable with a one-unit change in the predictor (independent) variable ("Bivariate Regression," 2005). Use of bivariate regression output, particularly the R Square statistic, would provide information useful in concluding to what extent the number of hours watching TV accounts for a persons annual income.

Description of Variables

Both variables are quantitative and measured at the interval-ratio level, as required in regression and correlation testing (Frankfort-Nachmias& Leon-Guerrero, 2015). The null hypothesis proposes that the number of hours watching TV (tvhoursvariable) is not related to respondent income (conrincvariable). Given this hypothesis, thetvhoursvariable is the independent, predictor variable. Theconrincvariable serves as the dependent, outcome variable.

Pearson Correlation Coefficient and Linear Regression

Given the number of cases within the data set, a scatter diagram of the relationship between variables is difficult to interpret (see Figure 1). A Pearson correlation coefficient and linear regression were calculated using SPSS Statistical Software to further explain and predict the relationship. SPSS output data are reported in Figure 2 below.

Figure 1.

Figure 2.

Correlations
	HOURS PER DAY WATCHING TV	RESPONDENT INCOME IN CONSTANT DOLLARS
HOURS PER DAY WATCHING TV	Pearson Correlation	1	-.177**
Sig. (2-tailed)		.000
N	1669	1001
RESPONDENT INCOME IN CONSTANT DOLLARS	Pearson Correlation	-.177**	1
Sig. (2-tailed)	.000
N	1001	1523
**. Correlation is significant at the 0.01 level (2-tailed).

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.177a	.031	.031	31222.277
a. Predictors: (Constant), HOURS PER DAY WATCHING TV

ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	31648218211.512	1	31648218211.512	32.465	.000b
Residual	973855744300.772	999	974830574.876
Total	1005503962512.284	1000
a. Dependent Variable: RESPONDENT INCOME IN CONSTANT DOLLARS
b. Predictors: (Constant), HOURS PER DAY WATCHING TV

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	40544.143	1538.265		26.357	.000
HOURS PER DAY WATCHING TV	-2596.520	455.703	-.177	-5.698	.000
a. Dependent Variable: RESPONDENT INCOME IN CONSTANT DOLLARS

The results of the Pearson correlation reveal a weak, negative correlation between hours watching TV and income (R=.177); as the number of hours watching TV increases, income decreases. In addition, I can a) conclude the correlation is statistically significant sincep=0.000 (alpha was set at 0.05), and b) reject the null hypothesis that there is no relationship between variables. Said differently, I can conclude there is enough evidence to suggest that the correlation observed does exist within the population.

Bivariate regression testing reveals an R Square of 0.031. From this statistic reported in the Model Summary, I conclude that only 3.1% of the respondents income is explained by the number of hours watching TV. Interpretation of the analysis of variance (ANOVA) output reveals statistical significance of the model with an F statistic of 32.465 and ap-value of 0.000 (alpha set at 0.05). This means that the regression model was statistically a better predictor of the relationship than just comparing variable means (Frankfort-Nachmias& Leon-Guerrero, 2015). Unstandardized coefficient output for the constant determined the Y intercept (a) to be 40544.143. Based on this output, I would conclude that the predicted income of respondents is approximately $40,544 when the number of hours watching TV is zero. The Beta value of -0.177 does not need to be interpreted since the analysis is bivariate in nature; Beta is interpreted in multiple regression situations (Frankfort-Nachmias& Leon-Guerrero, 2015). The slope coefficient for thetvhoursvariable, orb, is -2596.520. This statistic speaks to the gradient of regression and tells me that (on average) for every one hour increase in watching TV per day, a persons annual income decreases about $2,596. The level of significance for this model was 0.000 (less than alpha set at 0.05) suggesting that the predictor model that states an increase in watching TV results in a decrease in income is statistically significant.

Interpretation for Lay Audiences

The research question asked whether there is a statistically significant relationship between the number of hours one watches TV per day and their annual income. A hypothesis was tested that stated there would not be a relationship between hours watching TV and income. Based on statistical analysis completed using computer software, it was concluded that, although weak, there is a statistically significant relationship between watching TV and income, with only about 3% of income explained by the number of hours a person watches TV. To be more specific, it was concluded that a persons income goes down when the number of hours they spend watching TV increases per day. Based on the statistical analysis, it is predicted that for every one hour increase in the amount of time a person watches TV in a day on average, income decreases by about $2600 annually. It is not suggested here that watching TV causes a decrease in income; other variables may be in play and need to be considered (Frankfort-Nachmias& Leon-Guerrero, 2015; Rutter, 2011). It is only suggested that there is a relationship suggesting a correlation between the two variables and that, when examined more closely, suggests that when watching TV increases, income decreases.

Conclusion

Correlation and regression testing are commonly used methods for determining whether statistically significant relationships exists between metric-level variables (Rutter, 2011). In this discussion, I explored a research question and null hypothesis surrounding the relationship between the amount of time one watches TV to annual income. Pearson correlation testing determined that the relationship between variables, although weak and negatively correlated, was statistically significant. Income was reduced by about $2,600 for every unit increase in TV watching. I found this exercise beneficial in understanding how to determine the relationship, or correlation, between variables and how to determine the strength, or regression, of that relationship.

Kim

References

Bivariate regression coefficient. (2005). In W. P.Vogt(Ed.),Dictionary of statistics & methodology(3rd). SAGE Publications Ltd.http://dx.doi.org/10.4135/9781412983907

Data Set 2014 General Social Survey [Dataset file]. (2014). Retrieved fromhttps://class.waldenu.edu

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2015).Social statistics for a diverse society(7th ed.). Thousand Oaks, CA: Sage Publications, Inc.

Grove, S. K., Burns, N., & Gray, J. R. (2013).The practice of nursing research: Appraisal, synthesis, and generation of evidence(7th ed.). St. Louis: MO:Elsevier.

Kent State University. (2014). SPSS tutorials: Pearson correlations. Retrieved fromhttp://libguides.library.kent.edu/SPSS/PearsonCorr

Rutter, M. (2011). Proceeding from observed correlation to causal inference: The use of natural experiments.SAGE Quantitative Research Methods.http://dx.doi.org/10.4135/9780857028228"

Post 2

RSCH 8210 WK 8

Discussion

Mittie Hinz

Correlation and Bivariate Regression

Introduction

A bivariate analysisthe comparing of two groups which usually have a response variable (quantitative -dependent) and an explanatory variable (categorical or scale independent). It is common to compare means on the response variable for the categories of the dependent and independent variables (Agresti & Finlay, 2009). In the problem in this exercise the response/dependent variable is the respondents income in constant dollars (quantitative), depicted on the Y axis and the respondents highest year of school completed (scale), depicted on the X axis. The following scatter plot shows a tendency for respondents with higher degrees to earn more constant, higher incomes.

A correlationdescribes how strong the association is between the two variables and how closely the data follows a straight line trend. The slope of the line (b) shows the direction of the association; you want to know does the line slope upward (positive) or downward (negative)? This only shows the trend; it does not tell us the strength of the association. The correlation is denoted by r and is valid only when a straight line is a sensible model for the relationship, it measures the strength of the linear association between x and y. (-1

A regression analysisprovides a straight-line formula for predicting the values of the dependent variable from a given value of the independent variable.

Research Question

Is there a relationship between a respondents highest year of school completed and the respondents income in constant dollars?

Null hypothesiswould be there is no relationship between the highest year of school obtained and a respondents income in constant dollars.

Pearson Correlation Test

Is a bivariate test; bivariate correlation for respondents income in constant dollars and respondents highest level of education (interval ratio level - # of years of education). A Pearson correlation is easier to understand when two metric level variables are used (Laureate Educ., 2016b).

Correlations
	RESPONDENT INCOME IN CONSTANT DOLLARS	HIGHEST YEAR OF SCHOOL COMPLETED
RESPONDENT INCOME IN CONSTANT DOLLARS	Pearson Correlation	1	.353**
Sig. (2-tailed)		.000
N	1523	1523
HIGHEST YEAR OF SCHOOL COMPLETED	Pearson Correlation	.353**	1
Sig. (2-tailed)	.000
N	1523	2537
**. Correlation is significant at the 0.01 level (2-tailed).

Correlation coefficient of 0.353 between the highest year of school completed and their income in constant dollars.

Test of significancepvalue = .000 is well below the 0.05 confidence level, therefore we reject the null hypothesis that there is no relationship between the respondents highest year of school completed and their income in constant dollars.

We can tell from the Pearson correlation that this is a positive relationship. (range of values from -1 to +1, with a 0 indicating no relationship. The closer you move to 1 on either side, the stronger the relationship becomes. This correlation is significant at the 0.01 level (2-tailed).

Bivariate regression

Is similar to a Pearson which provides us the strength of a relationship between the two variables, the bivariate provides

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.353a	.125	.124	31246.915
a. Predictors: (Constant), HIGHEST YEAR OF SCHOOL COMPLETED

R is equal to the Pearson correlation coefficient

R²= 0.125 we can infer that 12.5% of the respondents income in constant dollars is explained by their highest year of school completed

ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	211453220920.304	1	211453220920.304	216.571	.000b
Residual	1485058299653.447	1521	976369690.765
Total	1696511520573.751	1522
a. Dependent Variable: RESPONDENT INCOME IN CONSTANT DOLLARS
b. Predictors: (Constant), HIGHEST YEAR OF SCHOOL COMPLETED

Testing for the overall significance of the regression model. Significance level of 0.000, which is below our 0.05 threshold. So model has statistical significance and R²can be interpreted.

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	-21258.539	3876.208		-5.484	.000
HIGHEST YEAR OF SCHOOL COMPLETED	3948.706	268.321	.353	14.716	.000
a. Dependent Variable: RESPONDENT INCOME IN CONSTANT DOLLARS

Constant = where the slope of regression line intercepts with the y-axis (respondent income in constant dollars)

Independent variable (highest year of school completed) every additional year of school completed the respondents income in constant dollars will change by 3948.706 units

Significance level of 0.000 is lower than 0.05 level and therefore we reject null hypothesis that there is no relationship between respondents income in constant dollars and the highest year of school completed. The more school one completes, on average, the higher the respondents income (Laureate Edu., 2016b).

Research Design

This would be a non-experimental, quantitative design testing the given variables relationship to each other; these are called correlational studies (Creswell, 2009, p. 12).

Explanation for Lay Audience

We are wondering if education has an effect on the income one can earn. We looked at the number of years of school completed and with statistical testing showed there was an association or relationship between a respondents educational level (the number of years or the highest year of school completed) and the constant income earning potential of the respondent. That means that the more years of education (years) the higher the income level (in constant dollars) an individual can earn.

References

Agresti, A. & Finlay, B. (2009).Statistical methods for the social sciences.Upper Saddle River,

NJ: Pearson Prentice Hall

Laureate Education (Producer). (2016b). Correlation and bivariate regression [Video file].

Baltimore, MD: Author