Answer:
The values of B₀, B₁, and B₂ for this sample are as follows:
B₀ (cons): 108.154869 (in thousands of dollars)
B₁ (mominc): 96.617518
B₂ (dadinc): 26930.5625
Interpretation:
B₀ (cons) represents the intercept, which is the child's income in adulthood when both mother's income (mominc) and father's income (dadinc) are zero. In this case, the child's income would be approximately $108,155 (in thousands of dollars).
B₁ (mominc) represents the coefficient for the mother's income. It indicates that for every $1,000 increase in the mother's income, the child's income is expected to increase by approximately $96.62 (in thousands of dollars).
B₂ (dadinc) represents the coefficient for the father's income. It suggests that for every $1,000 increase in the father's income, the child's income is expected to increase by approximately $26.93 million (in thousands of dollars). Please note that there seems to be a typo in the output; the value is likely meant to be $26.93.
Predicted income for a child whose parents both had zero income:
To calculate the predicted income for a child whose parents both had zero income, we substitute mominc = 0 and dadinc = 0 into the regression model:
kidinc = B₀ + B₁ * mominc + B₂ * dadinc
kidinc = 108.154869 + 96.617518 * 0 + 26930.5625 * 0
kidinc = 108.154869 (in thousands of dollars)
The predicted income for this child would be approximately $108,155.
Predicted income for a child with parents earning $40,000 per year:
To determine the predicted value of income for someone whose parents both earned $40,000 per year, we substitute mominc = $40,000 and dadinc = $40,000 into the regression model:
kidinc = B₀ + B₁ * mominc + B₂ * dadinc
kidinc = 108.154869 + 96.617518 * 40 + 26930.5625 * 40
(Note: The values of B₁ and B₂ need to be converted to dollars, not thousands of dollars, since the income variables are measured in thousands of dollars in the model.)
Is there a statistically significant relationship between father's income and children's subsequent adult income?
Yes, based on the results, there is a statistically significant relationship between father's income (dadinc) and children's subsequent adult income (kidinc). We can know this from the t-values and associated p-values for the coefficients in the regression model.
In this case, the t-value for B₂ (dadinc) is 5.56, and the associated p-value is less than 0.001 (given as 0.000 in the output). Since the p-value is below the common significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant relationship between father's income and children's subsequent adult income.
Step-by-step explanation: