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# Test whether age is a variable between education and hours worked

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However, here is the question:

Provide your findings of this analysis as you would in a research report.
Be specific in your analysis - start from the larger portion of the analysis and move to specifics. Restate the RQ; provide descriptive analysis (not needed unless you consider there is a key point here); ANOVA (fit); correlation analysis (could variables co-vary excessively); R-Square; coefficients - the key is to answer the question: is age a spurious variable and influence the relationship between education and hours worked?

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We can use multivariate regression analysis as a method to control the effect of the independent variable on the dependent variable. We will use the variable age ("AGE") as a control variable by calculating a bivariate regression analysis. We cannot calculate separate regression analyses; we need the model to examine the interaction of all the IVs. Use the following table provides the data and the SPSS tables are provided for your analysis.
Dependent Variable is Hours Worked (hrs1)
Model 1 Model 2
Education (educ) Unstandardized Coefficient 1.256 Unstandardized Coefficient .954
Significance Level .000 Significance Level .000
Age (age) Unstandardized Coefficient -.439
Significance Level .000
R-Square = .024 Adjusted R-Square = .118
Provide your findings of this analysis as you would in a research report.
Be specific in your analysis - start from the larger portion of the analysis and move to specifics. Restate the RQ; provide descriptive analysis (not needed unless you consider there is a key point here); ANOVA (fit); correlation analysis (could variables co-vary excessively); R-Square; coefficients - the key is to answer the question: is age a spurious variable and influence the relationship between education and hours worked?

Using SPSS software, the following charts are generated and provided for your use:

Table 1(a)

Table 1(a) provides the descriptive statistics of three variables. The variation is higher in the variable "NUMBER OF HOURS WORKED LAST WEEK" as compare to any other variable because the standard deviation is higher.

Table 1(b)

The above table that is table 1(b) tells us about the model fit, since the P-value of ANOVA table is 0.000 which is less than .05 so we can say that the regresson model is significant at 5% level of significance. It means the independent variables which we have choosen predicts the dependent variable well.

Table 1(c)

Table 1 (c) represents the correlation matrix between the number of hours worked last week, age of respondent and their highest year of school completed. The correlation between the number of hours worked last week and age of respondent is -0.325. The correlation between the interview length and the age of the respondents is not stronger than the other correlation between highest year of school completed and age of respondent which is -.115. These correlations are significant at 5% level of significance and have a inverse relationship. It means if one variable increases the other decreases and vice versa. The correlation between the number of hours worked last week and highest year of school completed is .153. Again the correlation between these two variables is not strong, but still significant at 5% level of significance and also the direct relationship between these two variables. It means if one variable increases the other also increases and vice versa.
Here independent variables are also correlated with each other which is not good for regression model because it creates the problem in the fitted regression model.

Table 1(d)

Table 1(e)

Table 1 (d) represents the model summary. R-square (Coefficient of determination) tells us the amount of variation (information) which the response variable (dependent variable) is explained by the linear relationship of the (explanatory variable) independent variable(s). In the given problem, it is observed that 11.9% ( =0.112) variability in NUMBER OF HOURS WORKED LAST WEEK is explained by its linear relationship with age of respondent and highest year of school completed. The remaining 88.8% of the information goes to error or a merge to some other factor which is not observable in the model. The R-square is low but the overall model is significant even at 5% level of significance as given in the table of ANOVA.
Table 1 (e) represents the estimated coefficients of the regression model along with their P-values and confidence intervals. From table 1 (e), the regression model can be written as:
NUMBER OF HOURS WORKED LAST WEEK = 34.216 - .439*Age of respondent + .954* highest year of school completed

As the P-value of Age is 0.000 meaning that the age plays a significant role for predicting the NUMBER OF HOURS WORKED LAST WEEK at 5% level of significance. If we increase the age by one year the time then the NUMBER OF HOURS WORKED LAST WEEK is will be decreased by .439 hours keeping other factors constant. The P-value of the highest year of school completed is 0.000 which means that the highest year of school completed also plays a significant role in predicting the dependent variable. If we increase one unit of the highest year of school completed, then the NUMBER OF HOURS WORKED LAST WEEK decreases by 0.954 hours.

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