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,"+ 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. x 99.2 101.2 102.6 103.1 105.3 107.2 108.5 110.7 y 28.9 27.8 26.9 25.1 22.9 21.4 20.8 19.7 x 112.0 112.2 113.8 114.0 115.2 115.3 119.9 16.9 18.8 15.9 16.9 12.8 13.5 11.0 LA USE SALT Relevant summary quantities are > x, - 1640.2 > >, - 299.3. > x,2 - 179,865.54. > x,, - 32.259.22. > >,2 - 6409.33. (a) Obtain the equation of the estimated regression line. (Round all numerical values to four decimal places.) y = 119.3385 - 0.9089x Create a scatterplot of the data and graph the estimated line. 30 125 125 30 . . 120 120 25 25 115 115 .. 20 20 110 110 15 105 105 15 100 100 10 10 -X 100 105 110 115 120 125 10 15 20 25 30 10 15 20 25 30 100 105 110 115 120 125 Does it appear that the model relationship will explain a great deal of the observed variation in y? Yes v v , the linear model explains a great deal of the variation in y since the accompanying fitted line plot does show a very strong, linear association between unit weight and porosity. (b) Interpret the slope of the least squares line. (Round your answer to four decimal places.) The slope tells us that a one-pof increase in the unit weight of a concrete specimen is associated with a 0.9989 * percentage point decrease in the specimen's predicted porosity. (c) Predict porosity when unit weight is 134? (Round your answer to two decimal places.) - -2.45 Why is it not a good idea to predict porosity when unit weight is 134? When we predict porosity for a unit weight of 134 (which is outside the scope of the data) the result is [negative v . which cannot v . happen in reality. (d) Calculate the residual corresponding to the first observation. (Round your answer to two decimal places.) -0.28(d) Calculate the residual corresponding to the first observation. (Round your answer to two decimal places.) -0.28 Calculate the residual corresponding to the second observation. (Round your answer to two decimal places.) 7.16 X (e) Calculate a point estimate of o. (Round your answer to two decimal places.) 116.47 X Interpret the above point estimate of o. The unit weights of concrete specimens deviate from the least squares line by approximately the square of the point estimate of sigma on average. O Porosity measurements deviate from the least squares line by approximately the square of the point estimate of sigma on average. Porosity measurements deviate from the least squares line by approximately the point estimate of sigma on average. O The unit weights of concrete specimens deviate from the least squares line by approximately the point estimate of sigma on average. O Porosity measurements deviate from sample mean porosity measurement by approximately the square of the point estimate of sigma on average. (f) What proportion of observed variation in porosity can be attributed to the approximate linear relationship between unit weight and porosity? (Round your answer to two decimal places.) 0.97 Need Help? Watch It