We have a sample size of 20 young adult males diagnosed with anorexia nervosa, explain, using your predictive multiple regression model, exactly how you would determine whether this model was “significant” in terms of predicting your selected outcome variable.
a. Include a discussion of the evaluation of R and R-squared.
b. Include a discussion of how you would evaluate the F value and associated p value.
c. Discuss how an evaluation of standardized coefficient (beta weights) would be important in interpreting your proposed model.
To determine whether the multiple regression model is significant in predicting your selected outcome variable (anorexia nervosa in this case), you can follow these steps:
a. Evaluation of R and R-squared:
1. Calculate the correlation coefficient, R, which measures the strength and direction of the relationship between the predictor variables and the outcome variable.
2. Interpret the value of R. If R is close to 1, it suggests a strong positive relationship, while a value close to -1 indicates a strong negative relationship. A value close to 0 suggests little or no relationship.
3. Calculate R-squared, which represents the proportion of variance in the outcome variable that can be explained by the predictor variables.
4. Interpret the value of R-squared. A higher R-squared indicates that a larger proportion of the variance in the outcome variable is explained by the predictor variables.
b. Evaluation of F value and associated p value:
1. Calculate the F value, which tests the overall significance of the regression model.
2. Determine the corresponding p-value, which indicates the likelihood of obtaining the observed F value under the null hypothesis.
3. Evaluate the p-value. If the p-value is less than the chosen significance level (typically 0.05), it suggests that the regression model is significant in predicting the outcome variable.
c. Evaluation of standardized coefficients (beta weights):
1. Calculate the standardized coefficients (beta weights) for each predictor variable in the regression model. These coefficients allow for the comparison of the relative importance and contribution of each predictor.
2. Interpret the magnitude and sign of the standardized coefficients. A positive coefficient indicates a positive relationship, while a negative coefficient indicates a negative relationship, assuming all other variables in the model are held constant.
3. Evaluate the significance of the standardized coefficients based on their respective p-values. If the p-value for a coefficient is less than the chosen significance level (e.g., 0.05), it suggests that the predictor variable is significantly associated with the outcome variable.
In summary, to determine the significance of the multiple regression model, you need to consider the evaluation of R and R-squared to assess the strength of the relationship, the evaluation of the F value and associated p-value to test the overall significance of the model, and the evaluation of standardized coefficients to interpret the importance and significance of each predictor variable in the model.