Question

This question requires the use of Python or other statistical software. Load the dataset titled Income Consumption Data.csv into a data farme. The dataset contains consumption (Y ) and income (Xi) (in thousands of dollars per year) for ten hypothetical individuals. (a) Regress consumption on the individual’s income. That is, use the OLS to estimate the following regression model: Yi = β0 + β1Xi + ui (2) Print your regression output. Is the effect of income on consumption statistically significant at α = 5% significance level?

Answer 1

This answer provides steps to perform a regression analysis using Python or statistical software on a given dataset. It explains the process of creating a scatter plot, calculating the least-squares line, interpreting the y-intercept, and determining the significance of the correlation coefficient.

Step-by-step explanation:

a. Scatter Plot:

Using income as the independent variable (X-axis) and consumption as the dependent variable (Y-axis), we can create a scatter plot to visually represent the relationship between the two variables.

b. Regression Equation:

To calculate the least-squares line, we need to find the equation in the form ŷ = a + bx. The equation represents the line of best fit for the scatter plot.

c. Y-Intercept:

The y-intercept, denoted as 'a' in the regression equation, represents the estimated consumption when income is zero. In this case, the y-intercept represents the amount that would be consumed even if income was zero.

d. Correlation Coefficient:

The correlation coefficient measures the strength and direction of the linear relationship between income and consumption. To determine if it is significant, we need to compare it to a critical value based on the desired level of significance (α = 5%).