Linear regression plots a line between our data that minimizes the least squared difference between the data points and the regression line (Wooldridge 2009). This model allows us to generate estimates of the magnitude of impact of a one-unit increase in our independent variable on our dependent variable on average in the population of interest (Moore, McCabe & Craig, 2009).
It makes a few key assumptions, mostly that the individuals—and specifically, the residuals, or the distances between these data points and the line—are independently and identically distributed (Wooldridge 2009). If these assumptions are met, this approach is the best linear unbiased estimator. This generalized linear model is the basis for other statistical procedures, like ANOVA and t-tests (Trochim 2006a).
We plan to analyze our data using this method of analysis to assess three research questions: how self-rated satisfaction on intrinsic, extrinsic, and overall job satisfaction scales, respectively, predicts satisfaction with employer benefits. Specifically, these variables are all continuous variables that measure how people rank their satisfaction on a range from 1 to 7.
In order to assess the extent to which intrinsic job satisfaction predicts satisfaction with benefits, we can fit the following regression line: where benefits is our dependent variable (or “y”), represents the constant, or the intercept; represents the coefficient associated with the effect of a unit increase in the intrinsic score, and is the error term for each individual in the regression.
Our results suggest that there is a small, positive, non-significant relationship between intrinsic satisfaction and benefits. Specifically, our intercept is 5.199 and the slope of the line, or the one unit difference in the intrinsic score, is 0.033.
In other words, a score of 0 on the intrinsic scale would be associated with a 5.2 (though this is out of the range of our data, since the scale does not go to 0), and a one unit increase in the intrinsic score would raise the benefits score, on average, by 0.032 points.
While the intercept is significantly different from 0 (p<0.001), the intrinsic variable is not significantly different than 0 (p=0.49). The correlation coefficient of this model, or the extent of the variation in the benefits outcome explained by theis model, is 0.016, which is quite small.
In order to assess the extent to which intrinsic job satisfaction predicts satisfaction with benefits, we can fit the following regression line: where benefits is our dependent variable (or “y”), represents the constant, or the intercept; represents the coefficient associated with the effect of a unit increase in the extrinsic score, and is the error term for each individual in the regression.
Our results suggest that there is a small, negative, significant relationship between extrinsic satisfaction and benefits. Specifically, our intercept is 6.35 and the slope of the line, or the one unit difference in the intrinsic score, is -0.19.
In other words, a score of 0 on the extrinsic scale would be associated with a 6.4 (though this is out of the range of our data, since the scale does not go to 0), and a one unit increase in the extrinsic score would lower the benefits score, on average, by -0.19 points.
The intercept and extrinsic score are both significantly different from 0 (p<0.001. The correlation coefficient of this model, or the extent of the variation in the benefits outcome explained by this model, is 0.42, which is quite large.
In order to assess the extent to which overall job satisfaction predicts satisfaction with benefits, we can fit the following regression line: where benefits is our dependent variable (or “y”), represents the constant, or the intercept; represents the coefficient associated with the effect of a unit increase in the overall score, and is the error term for each individual in the regression.
Our results suggest that there is a small, positive, non-significant relationship between overall satisfaction and benefits. Specifically, our intercept is 5.73 and the slope of the line, or the one unit difference in the overall score, is -0.13.
In other words, a score of 0 on the overall scale would be associated with a 5.7 (though this is out of the range of our data, since the scale does not go to 0), and a one unit increase in the overall score would lower the benefits score, on average, by -0.13 points. While the intercept is significantly different from 0 (p<0.001), the overall variable is not significantly different than 0 (p=0.18).
The correlation coefficient of this model, or the extent of the variation in the benefits outcome explained by this model, is 0.06, which is quite small.
The results were markedly different with respect to the direction and magnitude of the effect of the satisfaction scales. For example, intrinsic had a very small, positive effect, though it was not significant, while the other two scales had a negative relationship. It might be that the extrinsic perceptions of satisfaction are inversely related with benefits—for someone who really likes their work, benefits matter less.
However, for someone’s instrinsic satisfaction, benefits are positively associated—the intrinsicly happier with the job, the happier with the benefits. However, it could also be that the direction of the intrinsic variable is due to chance. It wasn’t significantly different from 0 and could be a function of small sample size.
The extrinsic regression produced a very high correlation coefficient, which further makes the point that its association with benefits satisfaction is strong. As mentioned earlier, it could be that extrinsic satisfaction and benefits are strongly correlated in a way that other factors are not necessary for explaining their effects.
Moore, D.S., McCabe G.P., Craig, B.A. (2009). Introductionto the practice of statistics.6th Ed.New York : W.H. Freeman.
Trochim, W.R. (2006a). Research Methods Knowledge Base. http://www.socialresearchmethods.net/kb/dummyvar.php Accessed 3 February 2011.
Trochim, W.R. (2006b). Research Methods Knowledge Base. http://www.socialresearchmethods.net/kb/genlin.php Accessed 3 February 2011.
Wooldridge, J.M. (2009). Introductory Econometrics. 4th Ed. Mason, OH: South-Western Cengage.
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