ENGINEERING DATA ANALYSIS course subject

An article gave a scatter plot along with the least squares line of x = rainfall volume (m ) and y = runoff volume (m ) for a particular location. The accompanying values were read from the plot. x 4 12 14 18 23 30 40 48 55 67 72 79 96 112 127 y 4 10 13 15 15 25 27 48 38 46 53 72 82 99 1 LA USE SALT (a) Does a scatter plot of the data support the use of the simple linear regression model? Yes, the scatterplot shows a reasonable linear relationship. O Yes, the scatterplot shows a random scattering with no pattern. O No, the scatterplot shows a reasonable linear relationship. O No, the scatterplot shows a random scattering with no pattern. (b) Calculate point estimates of the slope and intercept of the population regression line. (Round your answers to four decimal places.) slope 0.8421 X intercept -1.8663 X (c) Calculate a point estimate of the true average runoff volume when rainfall volume is 55. (Round your answer to four decimal places.) 40.2387 X ma (d) Calculate a point estimate of the standard deviation o. (Round your answer to two decimal places.) 4.78 x m (e) What proportion of the observed variation in runoff volume can be attributed to the simple linear regression relationship between runoff and rainfall? (Round your answer to four decimal places.) 0.9801 XFor the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data: x 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y 75.1 71.5 57.3 48.5 74.5 72.8 67.8 59.0 58.3 48.0 USE SALT (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.) y = 0.9874x - 31.6152 Interpret the slope. O A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. O A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope. O A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. (b) Calculate the coefficient of determination. (Round your answer to four decimal places.) 0.6449 1X Interpret the coefficient of determination. The coefficient of determination is the proportion of the observed variation in axial strength of asphalt samples of this type that can be attributed to its linear relationship with cube strength. O The coefficient of determination is the proportion of the observed variation in axial strength of asphalt samples of this type that cannot be attributed to its linear relationship with cube strength. O The coefficient of determination is the number of the observed samples of axial strength of asphalt that can be explained by variation in cube strength. O The coefficient of determination is the number of the observed samples of axial strength of asphalt that cannot be explained by variation in cube strength. (c) Calculate an estimate of the error standard deviation & in the simple linear regression model. (Round your answer to three decimal places.) 6.450 x MPa Interpret the estimate of the error standard deviation & in the simple linear regression model. O The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount greater than one error standard deviation. O The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount within two error standard deviations. O The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount greater than two error standard deviations. The model's prediction for axial strength will typically differ from the specimen's actual axial strength by an amount within one error standard deviation