Correlation, Simple Regression, and Multiple Regression Analysis

Week 5 Review
Student’s Name
Institutional Affiliation
Course Details
Instructor’s Name
Date of Submission
Week 5 Review
SUMMARY OUTPUT



















Regression Statistics









Multiple R

0.719543









R Square

0.517742









Adjusted R Square

0.512919









Standard Error

1.815685









Observations

102



















ANOVA










 

df

SS

MS

F

Significance F





Regression

1

353.9275

353.9275

107.3578

1.6E-17





Residual

100

329.671

3.29671







Total

101

683.5985

 

 

 















 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%


Intercept

12.79933

0.710838

18.00597

3.79E-33

11.38905

14.20961

11.38905

14.20961


11

-1.0053

0.097024

-10.3614

1.6E-17

-1.19779

-0.81281

-1.19779

-0.81281


The given data involves the correlation between job site, microns, and mean annual sick days per employee. A regression analysis has been conducted on this data, and the output is summarized below.The multiple R value is 0.7195, which indicates a strong positive correlation between the variables. The R-square value of 0.5177 means that 51.77% of the variation in mean annual sick days per employee is explained by the linear relationship with job site and microns. The adjusted R-square value of 0.5129 is similar to the R-square value and suggests that the model is robust.
The standard error value of 1.8157 indicates the degree of variation in the dependent variable that is not explained by the independent variables. The regression equation is significant with a p-value of 1.59919E-17, indicating that the independent variables are significantly related to the dependent variable.
The ANOVA table shows that the regression model is significant as the F-value of 107.3578 is much larger than 1, and the p-value is less than 0.05, indicating that the regression model is a good fit for the data. The coefficient for the intercept is 12.7993, which means that if job site and microns are zero, the mean annual sick days per employee will be 12.7993.
The coefficient for job site is -1.0053, indicating that an increase in job site by one unit will decrease the mean annual sick days per employee by 1.0053, holding other variables constant. Similarly, the coefficient for microns is not shown in the output, which suggests that it is not significant in the regression model.
The regression analysis output suggests that job site is a significant predictor of mean annual sick days per employee, while microns are not. The model can be used to predict the mean annual sick days per employee based on job site, although other factors not accounted for in this model could also contribute to the variation in mean annual sick days per employee.
Simple regression data analysis
SUMMARY OUTPUT

















Regression Statistics








Multiple R

0.937994








R Square

0.879832








Adjusted R Square

0.879286








Standard Error

160.4169








Observations

222

















ANOVA