Adding the Regression Results Scatter Plot -Myassignmenthelp.Com

Question: Discuss About The Adding The Regression Results Scatter Plot? Answer: Introducation In todays world, education is not a luxury anymore; rather it has become essential to compete in the corporate work society. The main purpose of this report is to understand the influence of duration of education on wages (Veramendi Humphries and Heckman 2016). In this report a linear regression analysis along with other statistical descriptive analyses has been conducted to determine the relationship between the number of years of education received and corresponding wages per hour. Background Education is considered to be an investment in terms of human capital, the distinct productivity that an individual can provide. Consequently, higher level education can be regarded as a greater capital and a more assured investment (Strauss and Strauss 2018). Thus, from an economists point of interest, comprehending the relation between wages and years of education through appropriate quantitative analysis is of paramount importance. Method A sample of size 100 has been considered for this particular report. Corresponding years of experiences and hourly wages are provided in the data set (Binabaj et al. 2014). The methodology of regression analysis has been used to test whether there is any association between the number of years an individual has received education and his or her hourly wage (Guvenen and Rendall 2015). Two descriptive tables, consisting of the respective means, medians, modes and the ranges of the two variables have been provided in this report to have a basic understanding of the nature of the data sets. Analysis of a scatter plot is also considered, where the years of education is considered as the independent variable. Results Two descriptive tables are provided for the two columns in the data. Mean, median, standard deviation long with range and the minimum and maximum values are presented in the table for the respective labels. Year of Education Mean 13.76 Standard Error 0.272704376 Median 13 Standard Deviation 2.727043761 Range 15 Minimum 6 Maximum 21 Earnings per hour Mean 22.3081 Standard Error 1.402143746 Median 19.39 Standard Deviation 14.02143746 Range 72.06 Minimum 4.33 Maximum 76.39 A scatter diagram has been constructed with years of education considered to be the independent variable. Thus it is plotted along the horizontal axis (X axis). The linear trend line along with the corresponding equation and the R-squared value are also shown in the graph. As per the linear trend line, it is evident that there exists a positive linear trend among the variables of concern. In other words, there exists a positive linear relation between years of education and earnings per hour. A detailed regression analysis table is provided to estimate the regression equation. As considered earlier, the regression equation is to be estimated is an equation of wages on education. Implying number of educational years is considered as the independent variable and the other variable is the dependent one (Austin and Steyerber 2015). The estimated regression equation is (as approximated from the scatter plot) In terms of the relevant subject it can be expressed as From the above equation, values of hourly wages can be calculated by putting in subsequent values of the number of years of education. The general formula for the regression equation of y on x is given by The slope or to be precise the regression coefficient is referred to the coefficient of the independent variable in the regression equation which is in the general equation. It is defined as the ratio of the vertical change with respect to the horizontal change, which is known as the rise over run. Basically, slope of a regression equation of y on x, portrays the change in y in accordance to the change in x. The linear regression equation of wages on education is given by Thus in case of the above equation, slope is 2.1238. Interpretation of the slope is that a year of education is needed to increase the hourly wages by units. From the scatter plot and the regression analysis table, it can be inferred that although there exists a very crude linear relation between the variables, there is very little association between the two. At least from the data provided, no such associations can be seen. From the regression table, the R-squared value is found to be 0.1706 (approximately). R-squared value represents the level of variation, in percentage, in the dependent variable that could be elucidated by the independent variable (Austin and Steyerberg 2015). Thus, in this case, total years of education by an individual can describe only 17.06% of the variation in the hourly wages of those individuals. Hence, it can be concluded from the regression equation that the goodness of fit is very poor. Predicted value of the wages for those who have 12 and 14 years of education are to be calculated using the calculation regression equation. Putting the values of x as 12 and 14, the values obtained are The difference in the hourly wages of individuals having 14 and 12 years of education as calculated by the regression equation is . Discussion In conclusion, the report depicts a small scale of association between the two relevant variables. Slope of the equation is 2.1238, which does not depict a very high steep, implying lees association. However, there exists a linear trend or regression line with 17.06% goodness of fitting. From the scatter plot it is evident that most of the data is concerned with those who have received education between 12 and 16 years. In spite of that, there is a distinct variation in the hourly wages (Bttner and Thomsen 2015). Apart from that only 100 sample observations have been provided which may not be appropriate to decide on such a wide and vast subject. With a higher number of samples and that too with more varied range of years of education, a much more precise conclusion could be obtained (Meyer and Thomsen 2016). The p-value indicates that the null hypothesis, which states that there exists a linear relation between the variables, should be rejected. Thus it is evident that there exists no linear relation among these variables. Recommendations The first recommendation would be to gather a more relevant and widely spread data. It has been made clear that this is an important subject matter to do research. Thus, proper statistical sampling techniques should be applied and relevant data must be gathered. Since most of the data has been collected with those who have received education from 12 to 16 years, it is obvious that the data has a certain sense of biasedness. Mean, median and mode of the number of years of education are much closer than those of earnings per hour. Thus appropriate normality tests should be carried out to check for the normality of the respective distributions (Park 2015). Education and wages clearly have a positive correlation but their relation is not linear. Thus appropriate regression analysis needs to be carried out find the relevant nature of relation among these variables. References Austin, P.C. and Steyerberg, E.W., 2015. The number of subjects per variable required in linear regression analyses.Journal of clinical epidemiology,68(6), pp.627-636. Binabaj, F.B., Farhangfar, H., Azizian, S., Jafari, M. and Hassanpour, K., 2014. Logistic Regression Analysis of Some Factors Influencing Incidence of Retained Placenta in a Holstein Dairy Herd.Iranian Journal of Applied Animal Science,4(2). Bttner, B. and Thomsen, S.L., 2015. Are we spending too many years in school? Causal evidence of the impact of shortening secondary school duration.German Economic Review,16(1), pp.65-86. Guvenen, F. and Rendall, M., 2015. Women's emancipation through education: A macroeconomic analysis.Review of Economic Dynamics,18(4), pp.931-956. Meyer, T. and Thomsen, S.L., 2016. How important is secondary school duration for postsecondary education decisions? Evidence from a natural experiment.Journal of Human Capital,10(1), pp.67-108. Moon, K.W., 2016. Adding the Regression Results in Scatter Plot. InLearn ggplot2 Using Shiny App(pp. 247-254). Springer International Publishing. Park, H.M., 2015. Univariate analysis and normality test using SAS, Stata, and SPSS. Strauss, V., and Strauss, V. (2018).Report: Does money matter in education?.Washington Post. Retrieved 25 January 2018, from https://www.washingtonpost.com/blogs/answer-sheet/post/report-does-money-matter-in- education/2012/01/05/gIQAM8AweP_blog.html?utm_term=.2cb6606468b2 Veramendi, G., Humphries, J.E. and Heckman, J.J., 2016.Returns to Education: The Causal Effects of Education on Earnings, Health and Smoking(No. id: 10908).