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(a) Construct a scatter plot of the data. Does a simple linear regression model appear to be plausible (b) Fit the simple linear regression model using least squares. Find an estimate of 2. (c) Predict fretting wear when viscosity x 30. (d) Obtain the tted value of y when x 22.0 and calculate the corresponding residual. 11-11. An article in the Journal of Environmental Engineering (Vol. 115, No. 3, 1989, pp. 608 619) reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage). y x y x y x 4.4 0.19 11.8 0.47 19.2 0.69 6.6 0.15 12.1 0.70 23.1 1.30 9.7 0.57 14.3 0.60 27.4 1.05 10.6 0.70 14.7 0.78 27.7 1.06 10.8 0.67 15.0 0.81 31.8 1.74 10.9 0.63 17.3 0.78 39.5 1.62
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(a) Fit a simple linear regression model with y green liquor Na2S concentration and x production. Find an estimate of 2. Draw a scatter diagram of the data and the resulting least squares tted model. (b) Find the tted value of y corresponding to x 910 and the associated residual. (c) Find the mean green liquor Na2S concentration when the production rate is 950 tons per day. 11-9. An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383 394) described a study investigating the relationship between noise exposure and hypertension. The following data are representative of those reported in the article. y x y x 1 60 5 85 0 63 4 89 1 65 6 90 2 70 8 90 5 70 4 90 1 70 5 90 4 80 7 6 90 9 2 80 7 3 80 6
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(a) Draw a scatter diagram of y (blood pressure rise in millimeters of mercury) versus x (sound pressure level in decibels). Does a simple linear regression model seem reasonable in this situation (b) Fit the simple linear regression model using least squares. Find an estimate of 2. (c) Find the predicted mean rise in blood pressure level associated with a sound pressure level of 85 decibals. 11-10. An article in Wear (Vol. 152, 1992, pp. 171 181) presents data on the fretting wear of mild steel and oil viscosity. Representative data follow, with x oil viscosity and y wear volume (10 4 cubic millimeters).
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(a) Draw a scatter diagram of the data. Does a simple linear regression model seem appropriate here (b) Fit the simple linear regression model using the method of least squares. Find an estimate of 2. (c) Estimate the mean chloride concentration for a watershed that has 1% roadway area. (d) Find the tted value corresponding to x 0.47 and the associated residual. 11-12. A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond y is thought to be a linear function of the age of the propellant x when the motor is cast. Twenty observations are shown in the table on the next page. (a) Draw a scatter diagram of the data. Does the straight-line regression model seem to be plausible (b) Find the least squares estimates of the slope and intercept in the simple linear regression model. Find an estimate of 2. (c) Estimate the mean shear strength of a motor made from propellant that is 20 weeks old. (d) Obtain the tted values yi that correspond to each ob served value yi. Plot yi versus yi, and comment on what this plot would look like if the linear relationship between
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