The attached images show linear regression analysis to evaluate the ability of independent variables full and part-time FTEs, number of Medicare certified beds and urban vs. rural setting to predict dependent variable, occupancy rate.
The attached images show linear regression analysis to evaluate the ability of independent variables full and part-time FTEs, number of Medicare certified beds and urban vs. rural setting to predict dependent variable, occupancy rate.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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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.
Question
The attached images show linear
How do you interpret these results, what are the basic assumptions for regression analysis?
Transcribed Image Text:### Variables Entered/Removed
#### Variables Entered/Removed Summary
This table documents the variables entered or removed in the regression model, as well as the method used for variable selection.
- **Model**:
- **Variables Entered**: The variables included are `Urban=1 Rural=0`, `F59 FTEs Part Time`, `F59 FTEs Full Time`, `Medicare Certified Beds`, `F33 FTEs Part Time`, `F33 FTEs Full Time`.
- **Variables Removed**: None.
- **Method**: Enter
- Notes:
- a. Dependent Variable: `OccRate`
- b. All requested variables entered.
### Model Summary
#### Model Summary Statistics
This table provides key indicators of the model's performance including the correlation coefficient and the goodness of fit measures.
- **Model**:
- **R**: 0.334
- **R Square**: 0.111
- **Adjusted R Square**: 0.098
- **Std. Error of the Estimate**: 16.15966
- **Notes:**
- a. Predictors: (Constant), Urban=1 Rural=0, F59 FTEs Part Time, F59 FTEs Full Time, Medicare Certified Beds, F33 FTEs Part Time, F33 FTEs Full Time
- b. Dependent Variable: `OccRate`
### ANOVA (Analysis of Variance)
#### ANOVA Table
The ANOVA table breaks down the variance in the dependent variable to test the overall significance of the model.
- **Model**:
- **Sum of Squares**
- **Regression**: 12874.868
- **Residual**: 102625.909
- **Total**: 115500.777
- **df** (degrees of freedom):
- **Regression**: 6
- **Residual**: 393
- **Mean Square**:
- **Regression**: 2145.811
- **Residual**: 261.135
- **F**: 8.217
- **Sig. (P-value)**: 0.000
- **Notes:**
- a. Dependent Variable: `OccRate`
- b. Predictors
![### Residual Analysis in Regression
#### Residual Statistics
The table below provides a statistical summary of the residuals:
| Residuals Statistics | Minimum | Maximum | Mean | Std. Deviation | N |
|----------------------|-----------|-------------|--------|-----------------|---|
| Predicted Value | 54.8814 | 110.5536 | 81.8834| 5.68048 | 400|
| Residual | -76.74610 | 36.51113 | .00000 | 16.03770 | 400|
| Std. Predicted Value | -4.753 | 5.047 | .000 | 1.000 | 400|
| Std. Residual | -4.749 | 2.259 | .000 | .992 | 400|
a. Dependent Variable: OccRate
- **Predicted Value**: This measures the values predicted by the regression model for the dependent variable (OccRate). The maximum predicted value is 110.5536, and the minimum is 54.8814.
- **Residual**: The residuals are the differences between the observed and predicted values. They range from -76.74610 to 36.51113.
- **Std. Predicted Value**: These values range from -4.753 to 5.047, with a mean of 0 and a standard deviation of 1.
- **Std. Residual**: This is the standardized residual, which is the residual divided by its standard deviation. The values range from -4.749 to 2.259.
#### Scatterplot: Standardized Residuals vs. Standardized Predicted Values
The scatterplot below represents the relationship between the standardized residuals and the standardized predicted values of the dependent variable, OccRate.
![Scatterplot]
**Scatterplot Analysis**
- **X-Axis (Regression Standardized Predicted Value)**: This axis represents the standardized predicted values. The values range from approximately -5.0 to 5.0.
- **Y-Axis (Regression Standardized Residual)**: This axis represents the standardized residuals. The values range from approximately -6.0 to 4.0.
Each point on the scatterplot corresponds to an observation in the dataset. The plot helps to visualize whether the residuals are](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc734b4fa-0a8f-4b64-ae0a-4092f7bda12a%2Fcebf2253-1ba9-4ba9-935d-ac11f364202e%2F9zchpyc_processed.png&w=3840&q=75)
Transcribed Image Text:### Residual Analysis in Regression
#### Residual Statistics
The table below provides a statistical summary of the residuals:
| Residuals Statistics | Minimum | Maximum | Mean | Std. Deviation | N |
|----------------------|-----------|-------------|--------|-----------------|---|
| Predicted Value | 54.8814 | 110.5536 | 81.8834| 5.68048 | 400|
| Residual | -76.74610 | 36.51113 | .00000 | 16.03770 | 400|
| Std. Predicted Value | -4.753 | 5.047 | .000 | 1.000 | 400|
| Std. Residual | -4.749 | 2.259 | .000 | .992 | 400|
a. Dependent Variable: OccRate
- **Predicted Value**: This measures the values predicted by the regression model for the dependent variable (OccRate). The maximum predicted value is 110.5536, and the minimum is 54.8814.
- **Residual**: The residuals are the differences between the observed and predicted values. They range from -76.74610 to 36.51113.
- **Std. Predicted Value**: These values range from -4.753 to 5.047, with a mean of 0 and a standard deviation of 1.
- **Std. Residual**: This is the standardized residual, which is the residual divided by its standard deviation. The values range from -4.749 to 2.259.
#### Scatterplot: Standardized Residuals vs. Standardized Predicted Values
The scatterplot below represents the relationship between the standardized residuals and the standardized predicted values of the dependent variable, OccRate.
![Scatterplot]
**Scatterplot Analysis**
- **X-Axis (Regression Standardized Predicted Value)**: This axis represents the standardized predicted values. The values range from approximately -5.0 to 5.0.
- **Y-Axis (Regression Standardized Residual)**: This axis represents the standardized residuals. The values range from approximately -6.0 to 4.0.
Each point on the scatterplot corresponds to an observation in the dataset. The plot helps to visualize whether the residuals are
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