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. The current minimum wage is $5.15. If an employee earns the minimum wage, how many complaints can that employee expect to receive? Is the regression coefficient statistically significant? How can you tell
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.
The current minimum wage is $5.15. If an employee earns the minimum wage, how many complaints can that employee expect to receive?
Is the regression coefficient statistically significant? How can you tell?
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf0fe595-5e94-4dda-8ec9-411bf4f3c584%2Fc9317ecb-91c4-4bc4-9bd7-1920ad93aff1%2F9rqml7g_processed.png&w=3840&q=75)
![Table 9: Coefficients
Coefficientsal
Unstandardized Coefficients Standardized Coefficients
Model
В
Std. Error
Beta
Sig.
1
(Constant)
20.2
4.357
4.636
.000
Hourly Wage
-1.20
.088
-.946
-13.636
.000
a. Dependent Variable: Number of Complaints](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf0fe595-5e94-4dda-8ec9-411bf4f3c584%2Fc9317ecb-91c4-4bc4-9bd7-1920ad93aff1%2Fnmbeo9_processed.png&w=3840&q=75)
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