To analyze and interpret the output from your regression analysis, let's break down each part of your question systematically.
Given Information:
- Regression output includes coefficients, p-values, and R-squared values.
- Key terms include coefficients for predictors (X variables) and their respective significance levels.
A. How many parameters do we have?
Answer: The number of parameters in a regression model is usually equal to the number of predictors (independent variables) plus 1 for the intercept. If you have listed 12 parameters with a co-efficient value, you have 11 predictors plus 1 intercept. So, there would be 12 parameters total.
B. Compute the coefficients of the model.
Answer: Based on the information provided:
- The coefficients of the model are given (assuming the first value is the intercept):
- Intercept: -0.550454
- Coefficient for X1: 5.399976
- Coefficient for X2: -0.916521
- Coefficient for X3: Not provided explicitly at this step.
These coefficients represent the expected change in the dependent variable (Y) for a one-unit increase in the respective independent variables, holding other variables constant.
C. Compute and interpret R-squared of the model.
The R-squared value is the proportion of the variance in the dependent variable that can be explained by the independent variables. Answer:
- R-squared: 0.0000.
Interpretation: A value of 0.0000 means that the independent variables of the model do not explain any of the variability in the dependent variable Y. This is an extremely low R-squared value and suggests that the model may not be a good fit for the data.
D. Compute the value of the variance of the error term.
Variance of the error term can often be derived from the residual variance in the regression output. Answer: You mentioned a value of 0.9595, which seems to be the variance of the error term.
E. Are the coefficients of X1, X2, and X3 statistically significant at a 90% confidence interval?
To determine statistical significance, we typically look at the p-values and compare them to the significance level (α = 0.10 for 90% confidence).
- For X1 (p-value = 0.0796602): Significant (p < 0.10)
- For X2 (p-value = 1.272274): Not significant (p > 0.10)
- For X3 (p-value = 1.440109): Not significant (p > 0.10)
Answer:
- X1 is statistically significant at the 90% confidence level because its p-value is less than 0.10.
- X2 and X3 are not statistically significant at the 90% confidence level because their p-values are greater than 0.10.
Conclusion
- The model has 12 parameters.
- The coefficients indicate their influence on the dependent variable.
- The R-squared indicates a very weak model fit.
- The variance of the error term suggests some level of spread in the residuals.
- Only X1 is statistically significant at the 90% confidence interval.
If you require further clarification or additional analysis, feel free to ask!