Question 1192414: Consider the following estimated regression: Y=output, X=labor-hours of work)
Y ̂_i=3⋅6+0.25x_i ; σ_u^2=(1.83) ̂,n=10
95% CI: (-1.22, 1.05) (0.16, 0.34)
Answer by CPhill(2264)   (Show Source):
You can put this solution on YOUR website! **1. Interpretation of the Regression Equation**
* **Ŷ_i = 3.6 + 0.25x_i**
* This equation represents the estimated regression line.
* 3.6 is the intercept: the estimated value of Y when X (labor-hours) is zero.
* 0.25 is the slope: it indicates that for every one-unit increase in labor-hours (X), the output (Y) is estimated to increase by 0.25 units.
**2. Interpretation of σ_u^2 = (1.83)**
* σ_u^2 represents the estimated variance of the error term (u) in the regression model.
* The error term captures the variability in the actual output (Y) that is not explained by the labor-hours (X). A higher variance indicates greater unexplained variation.
**3. Interpretation of 95% Confidence Intervals**
* **(-1.22, 1.05):** This likely represents the 95% confidence interval for the **intercept** of the regression line. We are 95% confident that the true population intercept lies within this range.
* **(0.16, 0.34):** This likely represents the 95% confidence interval for the **slope** of the regression line. We are 95% confident that the true population slope of the relationship between labor-hours and output lies within this range.
**In summary:**
The provided information gives a basic understanding of the estimated regression model, including the estimated coefficients, the variance of the error term, and 95% confidence intervals for the intercept and slope. This information can be used to make inferences about the relationship between labor-hours and output within the context of the model.
**Note:**
* The confidence intervals provide a range of plausible values for the true population parameters.
* The interpretation of the results depends on the specific units of measurement for output and labor-hours in the context of the study.
**Disclaimer:** This analysis is based on the limited information provided. A more comprehensive understanding would require access to the full dataset, a more detailed analysis, and consideration of any assumptions and limitations of the regression model.
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