Multiple Regression Essay Example | Topics and Well Written Essays - 1500 words

Multiple Regression - Essay Example We use a State-wide data set that includes a record of property crimes rates (CRIMES) as well as a record on per capita income (PINCOME), school dropout rates (DROPOUT), precipitation amounts (PRECIP), percentage of public aid recipients (PUBAID), population density (DENSITY), public aid for families with kids in terms of dollars received (KIDS), percentage of unemployed workers (UNEMPLOY), percentage of population living in urban areas. The methodology that we use is that of multiple regression analysis to obtain the magnitude and signs of the coefficients and t and F-tests obtain whether the respective coefficients are significant, individually, or jointly. The regression equation we estimate is the following: (1) Results In this section we present the results of the analysis. Table 1 presents the results of the estimation of equation (1). Table 1: Results of simple OLS regression, all variables included Before interpreting the coefficients we look at the individual and joint signi ficances of the estimated coefficients. From the upper right hand panel we find that F(8, 41) = 11.43 and prob>F =0.000. Recall that the null hypothesis of the f-test is that all coefficients are jointly zero. From the computed statistic and the associated p-value we reject the null hypothesis. Thus, at least one of the parameters is non-zero. Now, from the lower panel in table 1 looking at the 3rd column (t-values) and the 4th column (p values) we can identify which coefficients are significantly different from zero. The null hypothesis of the t-test is that the coefficient in question is equal to zero while the alternative hypothesis is that it is non-zero. Recall that the 5% critical value for the two-sided t-test is 1.96. Looking at the elements from column 3 and 4, we find that only the variables DROPOUT, DENSITY and and URBAN are associated with coefficients that are statistically significantly different from zero. We fail to find evidence in the data that suggests that the nu ll hypothesis is false for the rest of the coefficients as well as the intercept. The upper right hand corner also presents the R-squared and the adjusted R-squared values which show that the fit is decent (anything greater than 50% on these scales is considered decent). In table 2 below, we take a look at whether our results may have been affected by the presence of multi-collnearity. The t-tests of significance showed that there were two significant coefficients and this was further confirmed by the f-test. If multicollinearity is present to any worrisome degree, typically, although the f-test rejects the null, we fail to identify any statistically significant coefficients in the t-test. Thus, there is little evidence of multi-collinearity. Additionally, we also look at the VIFs in table 2 below. Observe that the mean VIF is only 2.46 and the VIF for PINCOME is a bit large (although significantly smaller than 10, the standard indicator of severe and worrisome multicollinearity). T able 2: Testing for presence of multi-colinearity, VIFs Now, we rerun the regression incorporating only the significant variables in the specification. The model is specified as follows: The results of this regression are presented in table 3. Table 3: Results of OLS estimation including only the significant variables Observe first from the table above that the signs and the significances of the included variables remain the same. That is

Key Messaging Template for clients audience clientfamily connections Research Paper

Key Messaging Template for clients audience clientfamily connections LCC - Research Paper Example However, any protection should not obscure the main objective, which should be to ensure the safety and positive development of children at all levels (Partland, 2012). The love and natural instinct you have for your children should not be limited to your control alone. There are many other entities like childcare providers, concerned citizens, and the government that are keen to help you provide the best for your children. Childcare is a challenging job that requires the utmost dedication, passion, and commitment. You can collaborate with us so that we support each other in our duties. Such collaboration can include providing feedback and insights on training, and actively participating in the training of childcare employees. You are encouraged to identify areas of weaknesses in training and to propose remedial measures to improve the quality and effectiveness of our services (Family Connections, 2015c). You can also contribute financially to the provision of childcare services and therefore ensure that your children receive the best care possible. Finally, parents who are knowledgeable in childcare (e.g., nurses and developmental psychologists) are encouraged to apply for training positions in our organizations so that you improve the overall level of services. Childcare services are often funded by the government, the private sector, or donors. Of the three, donors have been identified as having the greatest potential to improve childcare services. This is evident in their level of commitment to and focus on, quality and effective childcare services. When it comes to training of childcare services, you have numerous avenues through which you can impact childcare services (Family Connections, 2015b). First, you can provide more funds to governments and the private sector to facilitate the expansion and enhancement of training activities. You can also fund childcare providers directly instead of using intermediaries like the government