The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. Table 7: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .854a .730 .695 6.6235
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below.
Table 7: Model Summary
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|
1 |
.854a |
.730 |
.695 |
6.6235 |
|
a. Predictors: (Constant), Hourly Wage |
Table 8: ANOVA
|
ANOVAb |
||||||
|
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
|
1 |
Regression |
1918.458 |
1 |
1918.458 |
129.783 |
.000a |
|
Residual |
709.567 |
48 |
14.782 |
|
|
|
|
Total |
2628.025 |
49 |
|
|
|
|
|
a. Predictors: (Constant), Hourly Wage |
||||||
|
b. Dependent Variable: Number of Complaints |
Table 9: Coefficients
|
Coefficientsa |
||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
||
|
B |
Std. Error |
Beta |
||||
|
1 |
(Constant) |
20.2 |
4.357 |
|
4.636 |
.000 |
|
Hourly Wage |
-1.20 |
.088 |
-.946 |
-13.636 |
.000 |
|
|
a. Dependent Variable: Number of Complaints |
What proportion of variation in the number of complaints can be explained by hourly wages? From the results shown above, write the regression equation.
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