No-fines concrete, made from a uniformly graded coarse aggregate and a cement-water paste, is beneficial in areas prone to excessive rainfall because of its excellent drainage properties. The article "Pavement Thickness Design for No-Fines Concrete Parking Lots," J. of Trans. Engr., 1995: 476-484) employed a least squares analysis in studying how y = porosity (%) is related to x = unit weight (pcf) in concrete specimens. Consider the following representative data:

Relevant summary quantities are (xi = 1640.1, (yi = 299.8, (x2i = 179,849.73, (xiyi, = 32,308.59, (y2i = 6430.06.
a. Obtain the equation of the estimated regression line. Then create a scatter-plot of the data and graph the estimated line. Does it appear that the model relationship will explain a great deal of the observed variation in y?
b. Interpret the slope of the least squares line.
c. What happens if the estimated line is used to predict porosity when unit weight is 135? Why is this not a good idea?
d. Calculate the residuals corresponding to the first two observations.
e. Calculate and interpret a point estimate of s.
f. What proportion of observed variation in porosity can be attributed to the approximate linear relationship between unit weight and porosity?

99.0 101.1 102.7 103.0 105.4 107.0 108.7 110.8 y 28.8 27.9 27.0 25.2 22.8 21.5 20.9 19.6 2 124 113.6 113.8 115.1 115.4 120.0 y17.1 18.9 16.0 16.7 13.0 13.6 10.8