**Capella 4020 Assessment 3 Improvement Plan In-Service Presentation**

Student Name

Capella University

NURS-FPX 4020 Improving Quality of Care and Patient Safety

Prof. Name

Date

**Logical reasoning for the Multiple Regression**

Multiple regression is a statistical technique used to examine the relationship between a dependent variable and two or more independent variables. It allows us to assess how the independent variables collectively influence the dependent variable, while controlling for the effects of other variables.

**The problem: **

To investigate the relationship between hospital costs and patient age, risk factors, and patient satisfaction scores.

**Hypothesis: **

Null hypothesis (H₀): There is no significant relationship between age and the combination of cost, risk, and satisfaction.

Alternative hypothesis (H₁): There is a significant relationship between age and the combination of cost, risk, and satisfaction.

Statistical Significance and Effect Size of the Regression Coefficient |

**Table 1**

*Predictors: (Constant), satisfaction, risk, cost*

R | R Square | AdjustedR Square | Std. Error of the Estimate | R Square Change | F Change | df1 | df2 | Sig. F Change |

.315 | .099a | .084 | 6.15353 | .099 | 6.645 | 3 | 181 | .000 |

#### Capella 4020 Assessment 3

- Statistical Significance and Effect Size:
- The coefficient of determination (R-squared) is 0.099, indicating that approximately 9.9% of the variance in the dependent variable (age) can be explained by the independent variables (cost, risk, and satisfaction).
- The adjusted R-squared is 0.084, which takes into account the number of predictors and the sample size. It suggests that about 8.4% of the variance in age is accounted for by the independent variables, adjusted for the degrees of freedom.
- The F-test statistic is significant (p < 0.001), indicating that the overall regression model is statistically significant.

- Model Fit:
- The standard error of the estimate is 6.15353. It represents the average distance between the observed values and the predicted values by the regression model.
- The change statistics show that the inclusion of the independent variables (cost, risk, and satisfaction) in the model has resulted in a significant increase in R-squared.

The multiple regression model, including the independent variables (cost, risk, and satisfaction), is statistically significant in predicting age. However, the model has limited explanatory power, as only around 9.9% of the variance in age is accounted for by the independent variables. The adjusted R-squared suggests that when considering the degrees of freedom and sample size, the independent variables explain about 8.4% of the variance in age.

**Fit of the Regression Model**

The regression model used to predict age based on the variables of cost, risk, and satisfaction has a limited ability to explain the variance in age. The R-squared value of 0.099 indicates that only about 9.9% of the variability in age can be accounted for by these predictors. The adjusted R-squared value is 0.084, suggesting that the model’s predictive power does not improve substantially with the inclusion of additional predictors. While the overall model is statistically significant, as indicated by the F-test, noticing the effect size is relatively small. This states that there is a significant relationship between age and the predictors, the magnitude of the effect is limited.

**Caveats and Limitations:**

The low R-squared value indicates that there may be other factors influencing age that are not captured by the variables included in the model. Additionally, the standard error of the estimate indicates the average distance between the predicted and observed values, implying that there is still some unexplained variability in the model.

**Statistical Results of the Multiple Regression**

The statistical results of the multiple regression analysis can be applied to support a health care decision in numerous ways. In this analysis, we examined the relationship between age and three independent variables: cost, risk, and satisfaction. Let’s evaluate how these findings might aid and reveal healthcare managers in their decision-making.

- Resource Allocation: The significant effect of cost on age suggests healthcare managers should consider financial implications of age when allocating resources, enabling informed decisions on budget, resource allocation, and financial planning.
- Financial Planning: Health care organizations often need to plan for the future and anticipate the financial burden associated with age-related services. The regression analysis provides insights into the relationship between cost and age, enabling managers to project and estimate the financial resources required to meet the needs of an aging population.
- Service Planning and Design: The results of the analysis can guide managers in designing age specific healthcare services by considering the influence of cost on different age groups, ensuring that services are accessible and affordable.
- Risk Assessment: While the regression analysis did not find a statistically significant relationship between risk and age, healthcare managers should consider the potential impact of risk factors on age-related outcomes.

**Summary of the Results**

The multiple regression analysis investigated the relationship between age and three independent variables: cost, risk, and satisfaction. The results showed that only cost had a significant impact on age, while risk and satisfaction did not. This implies that cost is the most influential factor in determining age among the variables studied. However, the overall predictive power of the model was relatively weak. The statistical significance tests revealed that the coefficient for cost was statistically significant (p < 0.001), while the coefficients for risk and satisfaction were not (p > 0.05).

Cost appears to be a significant factor in determining age, but the model’s ability to predict age based on these variables is limited. The effect size analysis of the regression coefficients revealed that the standardized coefficient (Beta) for cost was 0.267, indicating that a one-unit increase in cost corresponds to a 0.267-unit increase in age, considering the other variables. On the other hand, the effect sizes for risk (0.095) and satisfaction (0.109) were relatively small, suggesting that these variables have less impact on age.

The fit of the regression model, as indicated by the R-squared value, showed that approximately 9.9% of the variation in age could be explained by the independent variables included in the model. This suggests that there are other unidentified factors that contribute to the variation in age, which were not accounted for in the analysis. The multiple regression analysis explored the relationship between age and variables such as cost, risk, and satisfaction. However, the study has limitations due to a limited dataset and the omission of other potential influencing factors.

The relatively low R-squared value suggests the existence of unmeasured variables affecting age. While cost has a significant impact on age, the effect size is relatively small. This underscores the complexity of age determination and highlights the need for further research to investigate additional factors comprehensively. Administrators should consider the financial implications of age but also account for other relevant factors when making age-related decisions.