res 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 ant summary quantities are Σχ. = 1640.2 Σy - 299,3, Σχε – 179,865.54, Σ×y, = 32,259,22, Σχε – 6409.33. 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. 125 y 120 115 110 x 112.0 112.2 113.8 114.0 115.2 115.3 119.9 y 16.9 18.8 15.9 16.9 12.8 13.5 11.0 105 100 O USE SALT 10 15 20 25 30 X y 125 120 115 110 105 100 O 10 15 20 25 Interpret the slope of the least squares line. (Round your answer to four decimal places.) The slope tells us that a one-pcf increase in the unit weight of a concrete specimen is associated with a -0.696 Calculate a point estimate of a. (Round your answer to two decimal places.) 3.87 x 30 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.) 3.01 X 30 25 Does it appear that the model relationship will explain a great deal of the observed variation in y? Yes ✓✓ , the linear model explains a great deal of the variation in y since the accompanying fitted line plot does 20 15 10 Predict porosity when unit weight is 134? (Round your answer to two decimal places.) 9--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 ✔✔✔ which cannot 100 105 110 115 120 x. 125 30 ✔happen in reality. 25 20 15 10 100 X percentage point decrease in the specimen's predicted porosity. 105 110 show a very strong, linear association between unit weight and porosity. 115 120 es

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