Efficient design of certain types of municipal waste incinerators requires that information about energy content of the waste be available. The authors of the article “Modeling the Energy Content of Municipal Solid Waste Using Multiple
Using Minitab to fit a multiple regression model with the four aforementioned variables as predictors of energy content resulted in the following output:
a. Interpret the values of the estimated regression coefficients
b. State and test the appropriate hypotheses to decide whether the model fit to the data specifies a useful linear relationship between energy content and at least one of the four predictors.
c. Given that % plastics, % paper, and % water remain in the model, does % garbage provide useful information about energy content? State and test the appropriate hypotheses using a significance level of .05.
d. Use the fact that
e. Use the information given in part (d) to predict energy content for a waste sample having the specified characteristics, in a way that conveys information about precision and reliability.
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Probability and Statistics for Engineering and the Sciences
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- A sixth-grade teacher believes that there is a relationship between his students’ IQscores (y) and the numbers of hours (x) they spend watching television each week. Thefollowing table shows a random sample of 7 sixth-grade students.y 125 116 97 114 85 107 105x 5 10 30 16 41 28 21 Does the data provide sufficient evidence to indicate that the simple linear regressionmodel is appropriate to describe the relationship between x and y? Perform a model utilitytest at α = 0.05. (Give H0, Ha, rejection region, observed test statistic, P-value, decisionand conclusion.)Find the Pearson sample correlation coefficient between x and y. Then interpretthe result.arrow_forwardA student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained. ANOVA df SSRegression 3 45.9634Residual 11 2.6218Total Coefficients Standard Error Intercept 0.0136x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 -Write out the estimated regression equation for the relationship between the variables. (1mark)-Compute coefficient of determination. What can you say about the strength of thisrelationship? -Carry out a test to determine whether y is significantly related to the independent variables.Use a 5% level of significance.-Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.arrow_forwardThe article “Models for Assessing Hoisting Times of Tower Cranes” (A. Leung and C. Tam, Journal of Construction Engineering and Management, 1999: 385–391) presents a model constructed by a stepwise regression procedure to predict the time needed for a tower crane hoisting operation. Twenty variables were considered, and the stepwise procedure chose a nine-variable model. The adjusted R2 for the selected model was 0.73. True or false: a) The value 0.73 is a reliable measure of the goodness of fit of the selected model. b) The value 0.73 may exaggerate the goodness of fit of the model. c) A stepwise regression procedure selects only variables that are of some use in predicting the value of the dependent variable. d) It is possible for a variable that is of no use in predicting the value of a dependent variable to be part of a model selected by a stepwise regression procedure.arrow_forward
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