1. **Problem Statement:** We are given data on U.S. Real Personal Consumption Expenditures (CON) and Real Disposable Personal Income (INCOME) from 1959 to 2007. We need to examine descriptive statistics, discuss the correlation between income and consumption, estimate the Ordinary Least Squares (OLS) regression equation, and validate the model. 2. **Descriptive Statistics and Variable Behavior:** - The summary statistics show a strong linear relationship between INCOME and CON. - The standard error of the regression (S) is 445.496, indicating the average distance that the observed values fall from the regression line. - The R-squared (R-Sq) is 99.37%, meaning that approximately 99.37% of the variability in consumption expenditures is explained by income. - The adjusted R-squared (R-Sq(adj)) is 99.35%, which adjusts for the number of predictors and confirms the model's high explanatory power. 3. **Correlation Between Income and Consumption Expenditures:** - The very high R-squared value suggests a strong positive correlation between income and consumption. - This means as income increases, consumption expenditures also increase in a nearly linear fashion. 4. **OLS Equation Estimation:** - The fitted regression line is given by: $$\text{CON} = 1480 + 1.015 \times \text{INCOME}$$ - Here, 1480 is the intercept ($\hat{\alpha}$), representing the estimated consumption when income is zero. - The slope 1.015 ($\hat{\beta}$) indicates that for each unit increase in income, consumption increases by approximately 1.015 units. 5. **Model Validation:** - The Analysis of Variance (ANOVA) table shows: - Regression sum of squares (SS) = 1466528970 - Error SS = 9327952 - Total SS = 1475856922 - The F-statistic is 7389.28 with a p-value of 0.000, indicating the model is statistically significant. - The small error SS compared to regression SS confirms the model fits the data well. 6. **Summary:** - The data shows a strong linear relationship between income and consumption. - The OLS regression model fits the data excellently with high R-squared and significant F-test. - The positive slope confirms that consumption increases with income.