7/23/2017 Question 1 1 pts 1) In the oil industry, water that mixes with crude oil during production and transportation must be removed. Chemists have found that the oil can be extracted from the water/oil mix electronically. Researchers at the University of Bergen (Norway) conducted a series of experiments to study the factors that inuence the voltage (Y) required to separate the water from the oil. There were 7 independent variables investigated in the study: X1 = the disperse phase volume, X2 = salinity, X3 = temperature, X4 = time delay, X5 = surfactant concentration, X6 = triton span, and X7 = percent of solid particles. Sixteen water/oil mixtures were prepared using dierent combinations of the independent variables, then each emulsion was exposed to a high electrical eld and the voltage needed to separate the oil and water was recorded. Note that this is an example of an experiment that was designed to determine which of the 7 independent variables have an eect upon the voltage required to separate the oil and water. a) The following output is from a regression model in which all of the seven possible independent variables are included in the model. Which of the variables help predict the voltage required to separate the water from the oil? Justify your answer. Choose the best answer from the following: i) All the variables are helpful in predicting the voltage required because the R-Sq value is relatively large. ii) The variables Salinity, Surf. Con., Span, and Solid Particles are helpful in predicting the voltage required because the coecients for these variables are larger than .05. iii) The variables that have p-values that are less than .05 are the ones that help predict the voltage required. These variables are DPV and Surf. Con. iv) The variables Salinity, DPV, and Surf. Con. are helpful in predicting the voltage required because their p-values are greater than .10. 1/1 7/23/2017 Question 2 1 pts 1b) The variables that do not aect the voltage (based upon the results of part a) were removed from the multiple regression model, the results of this model are given below. Based on this output do all the variables in this model aect the voltage? Justify your answer. Choose the best answer from the following: i) Both DVP and Surf. Con have p-values that are less than .05 thus both of these variables aect the voltage. ii) This model is not so good because the R-Sq value of 58.7% is not very large. iii) Neither of the variables in this model have an impact upon the voltage because their p-values are less than .05. 1/1 7/23/2017 Question 3 1 pts 1c) In the oil industry, water that mixes with crude oil during production and transportation must be removed. Chemists have found that the oil can be extracted from the water/oil mix electronically. Researchers at the University of Bergen (Norway) conducted a series of experiments to study the factors that inuence the voltage (Y) required to separate the water from the oil. There were 7 independent variables investigated in the study: X1 = the disperse phase volume, X2 = salinity, X3 = temperature, X4 = time delay, X5 = surfactant concentration, X6 = triton span, and X7 = percent of solid particles. Sixteen water/oil mixtures were prepared using dierent combinations of the independent variables, then each emulsion was exposed to a high electrical eld and the voltage needed to separate the oil and water was recorded. Note that this is an example of an experiment that was designed to determine which of the 7 independent variables have an eect upon the voltage required to separate the oil and water. What was learned from this experiment? Choose the best answer from the following: i) The independent (X) variables that they have available are not the best because the R-Sq value is not very large ii) The experimenters learned that two of the variables that they thought might aect the voltage required to separate out the water actually did aect the voltage. iii) The experimenters learned that 5 variables that they thought might aect the voltage did not have any impact upon the voltage needed to separate the water iv) Both ii) and iii) 1/1 7/23/2017 Question 4 1 pts 2) A supervisor is interested in developing a model to predict the amount of time it requires to process incoming shipments of chemicals in drums being delivered to his warehouse. He selects 20 incoming shipments and records the following data: Y = the number of minutes required to handle the shipment, X1 = the number of drums in the shipment, and X2 = the total weight (in hundreds of pounds) of the shipment. a) The following are a scatter plot of the time to handle the shipment versus the number of drums in the shipment and a scatter plot of the time to handle the shipment versus the weight of the shipment. Interpret these plots. Choose the best answer from the following: i) There is a positive linear relationship between the number of minutes to handle the shipment and the number of drums in the shipment. ii) There is a positive linear relationship between the number of minutes to handle the shipment and the weight of the shipment. iii) There is a negative linear relationship between the number of minutes to handle the shipment ant the number of drums in the shipment. iv) There is a negative linear relationship between the number of minutes to handle the shipment and the weight of the shipment. iii) Both i) and ii) are true. 1/1 7/23/2017 Question 5 1 pts Choose the best answer from the following: i) Beta1 is the change in the time to process the shipment if the number of drums increases by 1. It is not possible that Beta1 = 0 since this hypothesis is rejected because the p-value for testing this is less than .05. ii) Beta1 is the change in the time to process the shipment if the number of drums increases by 1 and the weight of the shipment is not changed. It is not possible that Beta1 = 0 since this hypothesis is rejected because the p-value for testing this is less than .05. iii) Beta1 is the change in the time to process the shipment if the number of drums increases by 1. It is possible that Beta1 = 0 since this hypothesis is not rejected because the p-value for testing this is less than .05. iv) Beta1 is the change in the time to process the shipment if the number of drums increases by 1 and the weight of the shipment is not changed. It is possible that Beta1 = 0 since this hypothesis is not rejected because the p-value for testing this is less than .05. 1/1 7/23/2017 Question 6 1 pts Choose the best answer from the following: i) 5.080 plus or minus 1.404 or ( 3.676, 6.484). ii) 5.080 plus or minus 7.886 or ( -2.806, 12.966). iii) 3.768 plus or minus 1.296 or ( 2.472, 5.064). iv) 3.768 plus or minus 7.348 or ( -3.580, 11.116). v) 3.324 plus or minus 6.564 or ( -3.240, 9.888). 1/1 7/23/2017 Question 7 1 pts 2d) If a shipment has 9 drums and weighs 9.5 (hundreds of pounds), then use the regression equation to predict the amount of time required to handle this shipment. Choose the best answer from the following: i) 84.86 ii) 85.51 iii) 52.81 iv) 70.78 v) none of these 1/1 7/23/2017 Question 8 1 pts 2e) What is the value of S? Write a short sentence explaining why S is important. Choose the best answer from the following: i) S = 5.61756. The smaller the value of S, the closer the observations are to the regression equation. ii) S = 5.61756. The smaller the value of S, the more accurate the predictions using the regression equation will be. iii) S = 5.61756. S is the estimated value of the standard deviation of the errors in the regression model. iv) All of i), ii), and iii) are true. v) None of i), ii), and iii) are true. 1/1 Question 9 1 pts 3) In this problem we consider again data on 392 vehicles in which we would like to describe the relationship between the miles per gallon (mpg) of these vehicles and the following independent variables. Displacement: Engine displacement (cu. inches), Horsepower: Engine horsepower, Weight: Vehicle weight (lbs.), and Year: Model year (modulo 100). a) The following are scatter plots of the mpg versus the independent variables. Comment on these plots. For each variable is there a relationship between mpg and the independent variable? Choose the best answer from the following: i) The plots of mpg versus displacement, mpg versus horsepower, and mpg versus weight look like a curved relationship. The graph of mpg versus year is a linear relationship. ii) There is a linear relationship between displacement and mpg, horsepower and mpg, weight and mpg and year and mpg. iii) The correlation coecient could be used instead of the plots to characterize the relationships between displacement and mpg, horsepower and mpg, weight and mpg, and year and mpg. iv) i) and iii) are both correct. v) ii) and iii) are both correct. Question 10 3b) Consider a multiple regression model that includes all the independent variables. The plot of the residuals versus the tted values is given below. Comment on this plot? Choose the best answer from the following: i) There is not any problem with this plot. ii) The curved pattern suggests a problem with the regression model. iii) The variance is not constant, this is a problem with the regression model. iv) There are some outliers, this is a problem with the regression model. v) Both ii) and iii) are true. vi) All of ii), iii) and iv) are true. 1 pts Question 11 1 pts 3c) It was suggested that it would be more appropriate to use the log of mpg as the dependent variable. The following are plots of log mpg versus the four dependent variables. Comment on these plots. Is there a relationship between log mpg and these variables? Describe this relationship. Choose the best answer from the following: i) The plots of mpg versus displacement, mpg versus horsepower, and mpg versus weight look like a curved relationship. The graph of mpg versus year is a linear relationship. ii) There is a linear relationship between displacement and mpg, horsepower and mpg, weight and mpg and year and mpg. iii) The correlation coecient could be used instead of the plots to characterize the relationships between displacement and mpg, horsepower and mpg, weight and mpg, and year and mpg. iv) i) and iii) are both correct. v) ii) and iii) are both correct. Question 12 1 pts 3d) The computer output for the multiple regression model with log mpg as the dependent variable and the four independent variables is given below. Choose the best answer from the following: i) Since the p-values for horsepower, weight, and year are all less than .05, this means that the hypothesis that all the Beta's = 0 can be rejected. This means that at least one of displacement, horsepower, weight, and year impact logmpg. ii) Since the p-values for horsepower, weight, and year are all less than .05, this means that the hypothesis that all the Beta's = 0 can be rejected. This means that all of displacement, horsepower, weight, and year impact logmpg. iii) The p-value for testing the null hypothesis that all the Beta's = 0 is 0.000 < .05 so this hypothesis is rejected. This means that at least one of displacement, horsepower, weight, and year impact logmpg. iv) The p-value for testing the null hypothesis that all the Beta's = 0 is 0.000 < .05 so this hypothesis is rejected. This means that all of displacement, horsepower, weight, and year impact logmpg. Question 13 1 pts 3e) Are all of the four X variables needed in this model? Justify your answer. Choose the best answer from the following: i) When testing the null hypothesis that all the Beta's = 0, the p-value is 0.000 which is less than .05, so this hypothesis is rejected. This means that all of displacement, horsepower, weight, and year impact logmpg. ii) The variables weight and year are needed in the model because their p-values are = 0.000. The other two variables are not needed. iii) The only variable that is needed in the model is displacement since it is the only variable with a p-value greater than .05. iv) The p-value for displacement (.796 ) is greater than .05, thus displacement is not needed in the model. All the other 3 variables have p-values that are less than .05, therefore they are needed in the model. Question 14 1 pts 3f) Write a short sentence describing the meaning of R-Sq Choose the best answer from the following: i) Since the R-Sq value is relatively large (87.3%) this is a good model and nothing should be changed in the model. ii) The R-Sq = 87.3%, this means that 87.3% of the variation in logmpg is explained by the 4 variables displacement, horsepower, weight, and year. iii) The R-Sq = 87.3%, this means that 87.3% of the variation in logmpg is explained by the 3 variables horsepower, weight, and year. iv) The R-Sq = 87.3%, this means that only three of the variables, horsepower, weight, and year are needed in the model. Question 15 1 pts 3g) The following is a plot of the residuals versus the tted values for the model with log mpg as the dependent variable. Comment on this plot. Does this plot suggest any problems with this model? Choose the best answer from the following: i) This plot looks much better than the plot of the residuals versus the tted values for the model when the Y variable was the mpg ii) This plot does not suggest any problems with this model iii) There are a lot of points associated with the tted values between 3.0 and 3.6 compared to the tted values between 2.4 and 2.8. This is a problem with the model. iv) Both i) and ii) are correct. v) Both i) and iii) are correct