The following regression equation estimates the relationship between the number of cups of hot chocolate sold (H) and number of swimmers (N) at the beach: H=252.8-2.05N (2.06) (-3.05) (t values are shown in parentheses) R^2= 0.45. a) Explain or interpret the regression coefficient of N, the t-values, and the coefficient of determination of this equation. b) How is it possible that more hot chocolate is sold when there are fewer people at the beach? Does this relationship suggest anything about the specification of the equation?
H=252.8-2.05N (2.06) (-3.05) R^2= 0.45 a) when the regression line is linear (y = ax + b) the regression coefficient 2.05 is the constant that represents the rate of change of one variable (H) as a function of changes in the other (N); the t-value is a test statistic for t-tests that measures the difference between an observed sample statistic and its hypothesized population parameter in units of standard error; the coefficient of determination R2 is a number that indicates how well data fit a statistical model, in our case R2 = 0.45 means, that the line does not fit all the data. b) It is possible that more hot chocolate is sold when there are fewer people at the beach, because the colder is the weather, the fewer are the swimmers and the more cups of hot chocolate is bought.