Final answer:
To interpret the coefficients and their statistical significance in a multiple regression, analyze the output, draw a scatter plot, calculate the least-squares line, find the correlation coefficient, and determine if a line is the best fit for the data.
Step-by-step explanation:
When running a multiple regression to predict the first born male child's height from the mother and father's height, the independent variable should be the mother and father's height, and the dependent variable should be the first born male child's height. To interpret the coefficients and their statistical significance, we need to look at the output from the regression.
The output will provide the values of the coefficients for the mother's height and father's height, as well as their standard errors and t-values. The coefficient represents the change in the dependent variable for every one-unit increase in the independent variable. The t-value measures the statistical significance of the coefficient.
To determine if there is a relationship between the variables, you can plot a scatter plot of the data. If there is a clear pattern or trend in the scatter plot, it suggests a relationship between the variables. If the correlation coefficient is close to 0, it indicates no relationship.
To calculate the least-squares line, use the regression equation: ŷ = a + bx, where ŷ is the predicted height, a is the y-intercept, b is the slope, and x is the independent variable (mother's or father's height). The correlation coefficient measures the strength and direction of the relationship between the variables. If the correlation coefficient is close to 1 or -1, it indicates a strong linear relationship.
To find the estimated average height for a 1-year-old or an 11-year-old, plug the values into the regression equation and solve for the predicted height.
Based on the scatter plot and the statistical tests, you can determine if a line is the best way to fit the data. If the scatter plot shows a clear linear trend and the correlation coefficient is significant, a line can be a good fit. Otherwise, a different type of relationship (such as a curve) may be more appropriate.