Statistics for Business & Economics, Revised (MindTap Course List)
12th Edition
ISBN: 9781285846323
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: South-Western College Pub
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Chapter 15.3, Problem 12E
a.
To determine
Compute
b.
To determine
Find
c.
To determine
Explain whether the estimated regression equation explain a large amount of the variability in the data.
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A study of the amount of rainfall and the quantity of air pollution removed produced the following data shown in table below:
Daily Rainfall
x (0.01 cm)
Particulate Removed
y (μg/m3)
7
126
7.9
129.3
7.5
125.3
9.2
120.2
10.8
116.7
5.8
119.2
5.6
138.7
2.7
147.5
9.2
110.3
Compute and interpret the coefficient of determination, and coefficient of correlation for the given data.
What will be the regression equation, when swapped depended and independent variable
Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero.
a
b1
X1
R2
The following estimated regression equation relating sales to inventory investment and advertising expenditures was given.
ŷ = 28 + 15x1 + 9x2
The data used to develop the model came from a survey of 10 stores; for those data, SST = 18,000 and SSR = 13,140.
1. Compute R2
2. Compute Ra2
3. The adjusted coefficient of determination shows that ____ % of the variability has been explained by the two independent variables.
Chapter 15 Solutions
Statistics for Business & Economics, Revised (MindTap Course List)
Ch. 15.2 - The estimated regression equation for a model...Ch. 15.2 - Consider the following data for a dependent...Ch. 15.2 - In a regression analysis involving 30...Ch. 15.2 - A shoe store developed the following estimated...Ch. 15.2 - The owner of Showtime Movie Theaters, Inc., would...Ch. 15.2 - The National Football League (NFL) records a...Ch. 15.2 - PC World rated four component characteristics for...Ch. 15.2 - The Cond Nast Traveler Gold List provides ratings...Ch. 15.2 - Waterskiing and wakeboarding are two popular...Ch. 15.2 - Prob. 10E
Ch. 15.3 - In exercise 1, the following estimated regression...Ch. 15.3 - Prob. 12ECh. 15.3 - In exercise 3, the following estimated regression...Ch. 15.3 - In exercise 4, the following estimated regression...Ch. 15.3 - In exercise 5, the owner of Showtime Movie...Ch. 15.3 - In exercise 6, data were given on the average...Ch. 15.3 - Prob. 17ECh. 15.3 - Prob. 18ECh. 15.5 - In exercise 1, the following estimated regression...Ch. 15.5 - Refer to the data presented in exercise 2. The...Ch. 15.5 - The following estimated regression equation was...Ch. 15.5 - In exercise 4, the following estimated regression...Ch. 15.5 - Prob. 23ECh. 15.5 - The Wall Street Journal conducted a study of...Ch. 15.5 - The Cond Nast Traveler Gold List for 2012 provided...Ch. 15.5 - In exercise 10, data showing the values of several...Ch. 15.6 - In exercise 1, the following estimated regression...Ch. 15.6 - Refer to the data in exercise 2. The estimated...Ch. 15.6 - In exercise 5, the owner of Showtime Movie...Ch. 15.6 - Prob. 30ECh. 15.6 - The American Association of Individual Investors...Ch. 15.7 - Consider a regression study involving a dependent...Ch. 15.7 - Consider a regression study involving a dependent...Ch. 15.7 - Management proposed the following regression model...Ch. 15.7 - Refer to the Johnson Filtration problem introduced...Ch. 15.7 - This problem is an extension of the situation...Ch. 15.7 - The Consumer Reports Restaurant Customer...Ch. 15.7 - A 10-year study conducted by the American Heart...Ch. 15.8 - Data for two variables, x and y, follow. xi 1 2 3...Ch. 15.8 - Data for two variables, x and y, follow. xi 22 24...Ch. 15.8 - Exercise 5 gave the following data on weekly gross...Ch. 15.8 - The following data show the curb weight,...Ch. 15.8 - Prob. 43ECh. 15.9 - Refer to the Simmons Stores example introduced in...Ch. 15.9 - In Table 15.12 we provided estimates of the...Ch. 15.9 - Community Bank would like to increase the number...Ch. 15.9 - Over the past few years the percentage of students...Ch. 15.9 - The Tire Rack maintains an independent consumer...Ch. 15 - The admissions officer for Clearwater College...Ch. 15 - The personnel director for Electronics Associates...Ch. 15 - A partial computer output from a regression...Ch. 15 - Recall that in exercise 49, the admissions officer...Ch. 15 - Recall that in exercise 50 the personnel director...Ch. 15 - The Tire Rack, Americas leading online distributor...Ch. 15 - The Department of Energy and the U.S....Ch. 15 - A portion of a data set containing information for...Ch. 15 - Fortune magazine publishes an annual list of the...Ch. 15 - Consumer Research, Inc., is an independent agency...Ch. 15 - Matt Kenseth won the 2012 Daytona 500, the most...Ch. 15 - Finding the Best Car Value When trying to decide...
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardGiven below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1=married, 0=otherwise), a dummy variable for head of household (Head: 1=yes, 0=no) and a dummy variable for management position (Manager: 1=yes, 0=no). We shall call this Model 1. The coefficient of partial determination (R2Yj.(All variables except j)) of each of the six predictors are, respectively, 0.2807, 0.0386, 0.0317, 0.0141, 0.0958, and 0.1201. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given. Refer to model 1. Which of the following is the correct null hypothesis to test…arrow_forwardTen observations were provided for a dependent variable y and two independent variables x1 and x2; for these data, SST = 15,189.8 and SSR = 14,056.9. (a) Compute R2. (Round your answer to three decimal places.) R2 = (b) Compute Ra2. (Round your answer to three decimal places.) Ra2 = (c) Does the estimated regression equation explain a large amount of the variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to one decimal place.) , after adjusting for the number of independent variables in the model, we see that % of the variability in y has been accounted for.arrow_forward
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