Regression analysis:
Introduction:
An increase in employee benefits is likely to increase job satisfaction levels, the AIU data set contains intrinsic, overall and extrinsic variables that measure employee satisfaction, using the benefits variable as the independent variable models that show the relationship between benefits and the job satisfaction variables are estimated. it is expected that as benefits increase then all the other variables will increase, meaning that when employees are satisfied with benefits such as wages and salaries then their satisfaction is likely to increase, therefore increasing benefits satisfaction will increase satisfaction levels.
1. Benefits variable versus intrinsic variable:
In this model the intrinsic variable is set as the dependent variable while the benefit variable is set as the independent variable, the estimated model take the form Yi = B0 + B1X where Y is intrinsic and X is benefits, it is expected that the value of B1 will be positive given that as benefits variable increase the intrinsic variable also increases, the following is a summary of the excel output. (Stuart, 1998)
Multiple R
0.215
R Square
0.046
Adjusted R Square
0.005
Standard Error
1.028
Observations
25.000
ANOVA
df
SS
MS
F
Significance F
Regression
1.000
1.183
1.183
1.120
0.301
Residual
23.000
24.298
1.056
Total
24.000
25.482
Coefficients
Standard Error
t Stat
P-value
Lower
95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
3.240
1.822
1.778
0.089
-0.530
7.009
-0.530
7.009
BENEFITS
0.349
0.330
1.058
0.301
-0.333
1.031
-0.333
1.031
2. Benefits variable versus extrinsic variable:
The extrinsic variable is set as the dependent variable while the benefit variable is set as the independent variable, the estimated model take the form Yi = B0 + B1X where Y is extrinsic and X is benefits, the following is a summary of the excel output
Multiple R
0.381
R Square
0.145
Adjusted R Square
0.108
Standard Error
0.971
Observations
25.000
ANOVA
df
SS
MS
F
Significance F
Regression
1.000
3.678
3.678
3.905
0.060
Residual
23.000
21.663
0.942
Total
24.000
25.342
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
8.235
1.721
4.786
0.000
4.675
11.79
4.675
11.79
BENEFITS
-0.615
0.311
-1.97
0.060
-1.259
0.029
-1.26
0.029
3. Benefits variable versus the overall variable:
For this model the overall variable is set as the dependent variable while the benefit variable is set as the independent variable, the estimated model take the form Yi = B0 + B1X where Y is overall and X is benefits, the following is a summary of the excel output
Multiple R
0.024
R Square
0.001
Adjusted R Square
-0.043
Standard Error
1.063
Observations
25.000
ANOVA
df
SS
MS
F
Significance F
Regression
1.000
0.015
0.015
0.013
0.910
Residual
23.000
25.984
1.130
Total
24.000
25.998
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
5.422
1.885
2.877
0.009
1.523
9.320
1.523
9.320
BENEFITS
-0.039
0.341
-0.114
0.91
-0.744
0.666
-0.74
0.666
4. Graphs:
The following are scatter diagrams for the estimated models, graphs show the estimated model, and the R squared value and the trend line. (Stuart, 1998)
Benefits variable versus intrinsic variable:
The chart shows that there is a positive relationship between intrinsic and benefit, the estimated model is Y = 3.2396 + 0.3489 X, where X is benefits and Y is intrinsic. The y intercept value is 3.2396 and the slope is 0.3486, The R squared value is 0.0484.
Benefits variable versus extrinsic variable:
The chart shows that there is a negative relationship between extrinsic and benefit, the estimated model is Y = 8.2347 – 0.6152 X, where X is benefits and Y is extrinsic. The y intercept value is 8.2347 and the slope is – 0.6152, The R squared value is 0.1451.
Benefits variable versus the overall variable:
The chart shows that there is a negative relationship between overall and benefit, the estimated model is Y = 5.4218 -0.0399 X, where X is benefits and Y is overall. The y intercept value is 5.4218 and the slope is -0.0399, The R squared value is 0.0006.
Similarities and differences:
Two the model have a negative slope value showing that there is a negative relationship between the dependent variable and the independent variable, however the first model has a positive slope showing that there is a positive relationship between variables. The second model (Benefits variable versus extrinsic variable) has the highest R squared value and therefore the correlation between the variables is high. (Stuart, 1998)
Conclusion:
The above analysis shows how the benefit variable can be used to predict satisfaction value, benefits is positively related to intrinsic while benefits versus extrinsic and benefits versus overall are negatively related. The second model benefits versus extrinsic has the highest R squared value although its slope value is negative.
References:
Alexander Stuart (1998). Statistics: An Introduction, New York: McGraw hill press
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