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Chapter 12: Q28E (page 732)

Question: Chemical plant contamination. Refer to Exercise 12.18 (p. 725) and the U.S. Army Corps of Engineers study. You fit the first-order model,E(Y)=尾0+尾1x1+尾2x2+尾3x3 , to the data, where y = DDT level (parts per million),X1= number of miles upstream,X2= length (centimeters), andX3= weight (grams). Use the Excel/XLSTAT printout below to predict, with 90% confidence, the DDT level of a fish caught 300 miles upstream with a length of 40 centimeters and a weight of 1,000 grams. Interpret the result.

Short Answer

Expert verified

With 90% accuracy, it can be concluded that the mean DDT level of fish will be between the interval (3.8650, 33.8956)

Step by step solution

01

Step-by-Step SolutionStep 1: Confidence interval interpretation

The 90% confidence interval for DDT level of fish caught 300 miles upstream with a length of 40 cm and weight of 1000 grams is given in the image as (3.8650, 33.8956). This means that with 90% accuracy, it can be concluded that the mean DDT level of fish will be between the interval (3.8650, 33.8956)

02

Predicted value interpretation

The predicted value of the DDT level of fish calculated here is also 18.8803 which lies within the interval indicating that the predicted value is close to the actual value with 90% accuracy.

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Most popular questions from this chapter

Question: Study of supervisor-targeted aggression. 鈥淢oonlighters鈥� are workers who hold two jobs at the same time. What are the factors that impact the likelihood of a moonlighting worker becoming aggressive toward his/her supervisor? This was the research question of interest in the Journal of Applied Psychology (July 2005). Completed questionnaires were obtained from n = 105 moonlighters, and the data were used to fit several multiple regression models for supervisor-directed aggression score 1y2. Two of the models (with R2-values in parentheses) are given below:

a. Interpret the R2-values for the models.

b. Give the null and alternative hypotheses for comparing the fits of models 1 and 2.

c. Are the two models nested? Explain.

d. The nested F-test for comparing the two models resulted in F = 42.13 and p-value < .001. What can you conclude from these results?

e. A third model was fit, one that hypothesizes all possible pairs of interactions between self-esteem, history of aggression, interactional injustice at primary job, and abusive supervisor at primary job. Give the equation of this model (model 3).

f. A nested F-test to compare models 2 and 3 resulted in a p-value > .10. What can you conclude from this result?

Question: Predicting elements in aluminum alloys. Aluminum scraps that are recycled into alloys are classified into three categories: soft-drink cans, pots and pans, and automobile crank chambers. A study of how these three materials affect the metal elements present in aluminum alloys was published in Advances in Applied Physics (Vol. 1, 2013). Data on 126 production runs at an aluminum plant were used to model the percentage (y) of various elements (e.g., silver, boron, iron) that make up the aluminum alloy. Three independent variables were used in the model: x1 = proportion of aluminum scraps from cans, x2 = proportion of aluminum scraps from pots/pans, and x3 = proportion of aluminum scraps from crank chambers. The first-order model, , was fit to the data for several elements. The estimates of the model parameters (p-values in parentheses) for silver and iron are shown in the accompanying table.

(A) Is the overall model statistically useful (at 伪 = .05) for predicting the percentage of silver in the alloy? If so, give a practical interpretation of R2.

(b)Is the overall model statistically useful (at a = .05) for predicting the percentage of iron in the alloy? If so, give a practical interpretation of R2.

(c)Based on the parameter estimates, sketch the relationship between percentage of silver (y) and proportion of aluminum scraps from cans (x1). Conduct a test to determine if this relationship is statistically significant at 伪 = .05.

(d)Based on the parameter estimates, sketch the relationship between percentage of iron (y) and proportion of aluminum scraps from cans (x1). Conduct a test to determine if this relationship is statistically significant at 伪 = .05.

Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to forecast movie box office revenue, Exercise 11.27 (p. 657). Recall that opening weekend box office revenue data (in millions of dollars) were collected for a sample of 24 recent movies. In addition to each movie鈥檚 tweet rate, i.e., the average number of tweets referring to the movie per hour 1 week prior to the movie鈥檚 release, the researchers also computed the ratio of positive to negative tweets (called the PN-ratio).

a) Give the equation of a first-order model relating revenue (y)to both tweet rate(x1)and PN-ratio(x2).

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c) Which b in the model, part a, represents the change in revenue (y)for every 1-unit increase in the PN-ratio(x2), holding tweet rate(x1)constant?

d) The following coefficients were reported:R2=0.945andRa2=0.940. Give a practical interpretation for bothR2andRa2.

e) Conduct a test of the null hypothesis, H0;尾1=尾2=0. Use伪=0.05.

f) The researchers reported the p-values for testing,H0;尾1=0andH0;尾2=0 as both less than .0001. Interpret these results (use).

Question: Write a first-order model relating to

  1. Two quantitative independent variables.
  2. Four quantitative independent variables.
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