Final Answer:
The constant of proportionality, -0.64, signifies the rate or strength of the inverse relationship between the variables in the example. A change of one unit in one variable corresponds to a decrease of 0.64 units in the other.
Step-by-step explanation:
In the given example, the least-squares regression line for predicting y from x is given by the equation y^ = 1.80s - 0.64x. The constant term (-0.64) in this equation is called the slope of the line, and it represents the change in y for a unit change in x. In other words, it measures the strength and direction of the linear relationship between x and y.
In this case, the slope (-0.64) is negative, which indicates that as the value of x increases, the value of y decreases. This means that there is an inverse relationship between x and y. The magnitude of the slope (-0.64) also indicates that for every one-unit increase in x, y decreases by 0.64 units, on average.
The constant term (1.80) in this equation is called the y-intercept, and it represents the value of y when x is equal to zero. In other words, it is the point where the regression line intersects the y-axis. In this case, when x is zero, y is equal to 1.80, which means that there is a positive intercept on the y-axis.
Overall, this regression line provides a simple and useful model for predicting the value of y based on a known value of x, with a high degree of accuracy due to its close fit to the data points. However, it should be noted that regression analysis is only valid for linear relationships between variables, and nonlinear relationships may require more complex models to accurately predict outcomes.