5.5.B—Interpret coefficients for the least-squares regression line model

Interpret coefficients for the least-squares regression line model.

• The coefficients of the least-squares regression line model (line of best fit) are the slope, b, and the y-intercept, a, because they are based on a sample of values.
• The slope of the least-squares regression line can be interpreted as the predicted increase or decrease in the response variable for a oneunit increase in the explanatory variable, and it should be interpreted in context.
• The y-intercept in the least-squares regression line is the predicted value of the response variable when the explanatory variable is equal to 0, and it should be interpreted in context. Sometimes, the y-intercept of the line does not have a reasonable interpretation in context because x =0 might be beyond the interval of x-values used to determine the regression line (extrapolation). At other times, the y-intercept of the line does not have a logical interpretation in context because it might be a negative value for a response variable that has no negative values, such as height.