Final answer:
The least-squares regression line equation has a general form of y = a + bx. The exact values of the intercept (a) and slope (b) are derived from data, and for a negative slope, an increase in the independent variable (temperature) decreases the dependent variable (heat loss percentage).
Step-by-step explanation:
The equation for the least-squares regression line is a statistical tool used to predict the value of a dependent variable (represented as y) based on the value of an independent variable (represented as x). Given the context of predicting beak heat loss as a percentage of total body heat loss from temperature, the general form of the regression equation is y = a + bx, where a is the y-intercept and b is the slope of the line.
The values of the intercept and the slope must be calculated from the given dataset using statistical software or a calculator. Once these values are obtained, the least-squares regression line can be written in decimal notation with the intercept and slope to three decimal places. For example, if the calculated slope (b) is -0.303 and the y-intercept (a) is 31.930, then the equation of the regression line would be y = 31.930 - 0.303x.
It's important to understand that the slope of the line indicates how the dependent variable (y) changes for a one-unit increase in the independent variable (x). In the case of predicting heat loss from temperature, a negative slope would indicate that as temperature increases, the percentage of heat loss decreases.