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statistical techniques in business

Questions and Answers of Statistical Techniques in Business

Using software, conduct the repeated-measures ANOVA of the anorexia data in Table 12.18 (page 373), available at the text website. Interpret results.
The General Social Survey asks respondents to rate various groups using the “feeling thermometer” on a scale of 0 (most unfavorable) to 100 (most favorable).We plan to study how the mean compares
Recently the General Social Survey asked respondents,“Compared with 10 years ago, would you say that American children today are (1) much better off, (2) better off, (3) about the same, (4) worse
Refer to Table 12.15 (page 370) about the influence of three entertainment types on children.(a) Using software, conduct the repeated-measures analyses of Section 12.5.(b) Suppose you scored the
For the 2014 GSS, Table 12.32 shows sample means of political ideology (higher values being more conservative), classified by gender and by race, for those over 50 in age. For H0: no interaction,
The prediction equation ˆy = 16+2s+3r+8(s×r)relates y = annual income (thousands of dollars), s = sex(s = 1 for men, s = 0 for women), and r = race (r = 1 for whites, r = 0 for blacks). By finding
The 26 students in a statistics class for social science majors at the University of Florida were surveyed about their attitudes toward divorce. Each received a response score according to how many
Table 12.30 shows results of an ANOVA on y =depression index by gender and marital status (married, never married, divorced). State the sample size and fill in the blanks in the ANOVA table.
Table 12.29 summarizes responses on political ideology in the 2014 General Social Survey by religion and sex. The P-value is
In 2013, the U.S. Census Bureau reported that the population median income was $29,127 for white females,$26,006 for black females, $41,086 for white males, and$30,394 for black males.(a) Identify
In the United States, the Bureau of Labor Statistics recently reported that for males the current population mean hourly wage is $22 for white-collar jobs, $11 for service jobs, and $14 for
For the 2014 GSS, when we regress y = number of hours per day watching TV on s = sex (1 = male, 0 = female)and religious affiliation (r1 =1 for Protestant, r2 = 1 for Catholic, r3 = 1 for Jewish, r1
Using software with the Housesdata set at the text website, conduct an ANOVA for y = house selling price with factors whether the house is new and whether number of bathrooms exceeds two.(a) Using α
Table 12.13 on page 368 gave the prediction equationˆy = 5.23 − 1.77p1 − 1.24p2 − 0.01s relating political ideology to political party ID and to sex. Find the estimated means for the six
A recent GSS asked, “What is the ideal number of kids for a family?” Table 12.28 shows results of evaluating the effects of gender and race.(a) Explain how to interpret the results of the F
The sample means were 2.66 for white females, 2.62 for white males, 3.48 for black females, and 3.14 for black males. Explain how these results seem to be compatible with the results of the tests
When we use the GSS to evaluate how the mean number of hours a day watching TV depends on sex and race, for subjects of age 18–25, we get the results shown in Table
A recent GSS asked, “Would you say that you are very happy, pretty happy, or not too happy?” and “About how many good friends do you have?” Table 12.26 summarizes results, with number of
For g groups with n = 100 each, we plan to compare all pairs of population means.We want the probability to equal at least 0.80 that the entire set of confidence intervals contains the true
In a study to compare customer satisfaction at service centers for PC technical support in San Jose(California), Toronto (Canada), and Bangalore (India), each center randomly sampled 100 people who
Refer to the previous exercise.(a) Suppose that the first observation in the second group was actually 9, not 1. Then, the standard deviations are the same, but the sample means are 6, 7, and 8
Table 12.24 shows scores on the first quiz (maximum score 10 points) in a beginning French course. Students in the course are grouped as follows:Group A: Never studied foreign language before, but
A recent GSS asked, “How often do you go to a bar or tavern?” Table 12.23 shows descriptive statistics and an ANOVA table for comparing the mean reported number of good friends at three levels of
Refer to the previous exercise. Table 12.22 shows an ANOVA table for the model.(a) Specify the hypotheses tested in this table.(b) Report the F test statistic value and the P-value. Interpret the
A recent General Social Survey asked, “What is the ideal number of kids for a family?” Show how to define dummy variables, and formulate a model for this response with explanatory variable
A General Social Survey asked subjects how many good friends they have. Is this associated with the respondent’s astrological sign (the 12 symbols of the zodiac)?The ANOVA table for the GSS data
For GSS data comparing the reported number of good friends for those who are (married, widowed, divorced, separated, never married), an ANOVA table reports F = 0.80.(a) Specify the null and
Adjusted R2 is defined aswhere s2 is the estimated conditional variance and s2y is the sample variance of y, both of which are unbiased. This relates to ordinary R2 by(a) Suppose R2 = 0.339 for a
Let R2y(x1,... xp) denote R2 for the multiple regression model with p explanatory variables. Explain why Pyxxxp-1 R y(1p) 1-R2 R y(p-1) y(x1.Xp-1)
The numerator R2 – r2 yx1 of the squared partial correlation r2 yx2·x1 gives the increase in the proportion of explained variation from adding x2 to the model. This increment, denoted by r2
Refer to the previous exercise. When we add an interaction term, we get ˆy = −16.6 + 66.6x1 − 31.8x2 +29.4(x1x2).(a) Interpret the fit by reporting the prediction equation between selling price
Chapters 12 and 13 show how to incorporate categorical explanatory variables in regression models. This exercise provides a preview. Table 11.25 shows some output for a model for the Houses2 data set
Let ¯b∗i denote the estimated standardized regression coefficient when xi is treated as the response variable and y as an explanatory variable, controlling for the same set of other variables.
Software reports four types of sums of squares in multiple regression models. The Type I sum of squares, sometimes called sequential SS, represents the variability explained by a variable,
Suppose the correlation between y and x1 equals the multiple correlation between y and x1 and x2. What does this imply about the partial correlation ryx2·x1?Interpret.
Which of the following sets of correlations would you expect to yield the highest R2-value? Why?(a) ryx1= 0.4, ryx2= 0.4, rx1x2= 0.0.(b) ryx1= 0.4, ryx2= 0.4, rx1x2= 0.5.(c) ryx1= 0.4, ryx2= 0.4,
Whenever x1 and x2 are uncorrelated, then R2 for the model E(y) = α+β1x1+β2x2 satisfies R2 = r2 yx1+r2 yx2 .In this case, draw a figure that portrays the variability in y, the part of that
For the models E(y) = α + βx and E(y) =α + β1x1 + β2x2, express null hypotheses in terms of correlations that are equivalent to the following:(a) H0: β = 0.(b) H0: β1 = β2 = 0.
Give an example of three variables for which you expect β = 0 in the model E(y) = α + βx1 but for which it is plausible that β1 = 0 in the model E(y) = α + β1x1 + β2x2.
Let y = height, x1 = length of right leg, and x2 =length of left leg. Describe what you expect for the relative sizes of rx1x2, ryx2, R, and ryx2·x1.
Explain the difference in the purposes of the correlation, the multiple correlation, and the partial correlation.
The F test for comparing a complete model to a reduced model can be used to test(a) The significance of a single regression parameter in a multiple regression model.(b) H0: β1 = · · · = βp = 0
If ˆy = 2 + 3x1 + 5x2 − 8x3,(a) ryx3 < 0.(b) ryx3·x1 < 0.(c) ryx3·x1,x2 < 0.(d) Insufficient information to answer.(e) Answers (a), (b), and (c) are all correct.
If ˆy = 2 + 3x1 + 5x2 − 8x3,(a) The strongest correlation is between y and x3.(b) The variable with the strongest partial influence on y is x2.(c) The variable with the strongest partial influence
If ˆy = 2 + 3x1 + 5x2 − 8x3, then controlling for x2 and x3, the predicted mean change in y when x1 is increased from 10 to 20 equals(a) 3, (b) 30, (c) 0.3, (d) cannot be given—depends on
In regression analysis, which of the following statements must be false? Why?(a) ryx1= 0.01, ryx2= −0.75, R = 0.2(b) The value of the residual sum of squares, SSE, can increase as we add additional
Table 11.24 shows results of fitting various regression models to data on y = college GPA, x1 = high school GPA, x2 = mathematics entrance exam score, and x3 =verbal entrance exam score. Indicate
In Exercise 11.1 on y = college GPA, x1 = high school GPA, and x2 = college board score, E(y) = 0.20 + 0.50x1 + 0.002x2. True or false: Since β1 = 0.50 is larger than β2 = 0.002, this implies that
An article11 that analyzed the effects of the levels of the participant’s generosity and of the spouse’s generosity on a measure of marital quality reported that low levels of both were
An article10 used multiple regression to predict a measure of tolerance toward homosexuality.(a) The researchers found that the effect of number of years of education varied from essentially no
The Economist magazine9 developed a quality-oflife index for nations as the predicted value obtained by regressing an average of life-satisfaction scores from several surveys on gross domestic
A study8 relating the percentage of a child’s life spent in poverty to the number of years of education completed by the mother and the percentage of a child’s life spent in a single-parent home
A study7 of mortality rates found in the United States that states with higher income inequality tended to have higher mortality rates. The effect of income inequality disappeared after controlling
For Example 11.2 on mental impairment, Table 11.21 shows the result of adding religious attendance as an explanatory variable, measured as the approximate number of times the subject attends a
Analyze the Houses data file at the text website(and introduced in Example 9.10 on page 268), using selling price of home, size of home, number of bedrooms, and taxes. Prepare a one-page report
In about 200 words, explain to someone who has never studied statistics what multiple regression does and how it can be useful.
For the UN data file at the text website (Table 3.9 on page 53), construct a multiple regression model containing two explanatory variables that provide good predictions for the fertility rate. How
For the previous exercise, repeat the analysis, excluding the observation forD.C. Describe the effect of this observation on the various analyses.
Using software with the Crime data file at the text website, conduct a regression analysis of violent crime rate with the explanatory variables poverty rate, the percentage living in urban areas, and
For the OECD data file at the text website, shown in Table 3.13 (page 58), pose a research question about how at least two of the variables shown in that table relate to carbon dioxide emissions.
Using industry-level data, a recent study6 analyzed labor’s share of income, measured as total compensation divided by total compensation plus the gross operating surplus. The authors predicted
Refer to the student data file created in Exercise 1.12. For variables chosen by your instructor, fit a multiple regression model and conduct descriptive and inferential statistical analyses.
Refer to the Students data file. Using software, conduct a regression analysis using either (a) y = political ideology with explanatory variables number of times per week of newspaper reading and
A recent study5 analyzed the effect of x1 = work hours per day and x2 = commuting time to work on y = political participation. For the cluster sample of 1001 adult Americans, ¯x1 = 8.4 hours (s =
Amultiple regression model describes the relationship among a collection of cities between y = murder rate(number of murders per 100,000 residents) and x1 =number of police officers (per 100,000
For the 2014 GSS, Table 11.20 shows estimates(with se values in parentheses) for four regression models for y = political party identification in the United States, scored from 1 = strong Democrat to
Refer to Examples 11.1 (page 308) and 11.8(page 331). Explain why the partial correlation between crime rate and high school graduation rate is so different(including its sign) from the bivariate
Refer to the previous exercise.(a) Find the partial correlation between y and x1, controlling for x2. Interpret the partial correlation and its square.(b) Find the estimate of the conditional
Table 11.19 shows results of regressing y = birth rate (number of births per 1000 population) on x1 =women’s economic activity and x2 = literacy rate, using UN data for 23 nations.(a) Report the
A multiple regression analysis investigates the relationship between y = college GPA and several explanatory variables, using a random sample of 195 students at Slippery Rock University. First, high
Use software with the Houses data file to allow interaction between number of bedrooms and number of bathrooms in their effects on selling price.(a) Interpret the fit by showing the prediction
A study analyzes relationships among y = percentage vote for Democratic candidate, x1 = percentage of registered voters who are Democrats, and x2 = percentage of registered voters who vote in the
Exercise 11.11 showed a regression analysis for statewide data on y = violent crime rate, x1 = poverty rate, and x2 = percentage living in urban areas. When we add an interaction term, we get ˆy =
Refer to the previous exercise.(a) Test the partial effect of number of bathrooms, and interpret.(b) Find the partial correlation between selling price and number of bathrooms, controlling for number
Use software with the Houses data file at the text website to conduct a multiple regression analysis of y =selling price of home (dollars), x1 = size of home (square feet), x2 = number of bedrooms,
Refer to the previous exercise. Find a 95% confidence interval for the change in the mean of y for a(a) 1-unit increase, (b) 50-unit increase in the percentage of adults owning homes, controlling for
For a random sample of 66 state precincts, data are available on y = percentage of adult residents who are registered to vote, x1 =percentage of adult residents owning homes, x2 = percentage of adult
Refer to Table 11.5 on page 316. TestH0: β2 = 0 that mental impairment is independent of SES, controlling for life events. Report the test statistic, and report and interpret the P-value for (a) Ha:
The General Social Survey has asked subjects to rate various groups using the “feeling thermometer.” The rating is between 0 and 100, more favorable as the score gets closer to 100 and less
Table 11.16 comes from a regression analysis4 of y = number of children in family, x1 = mother’s educational level in years (MEDUC), and x2 = father’s socioeconomic status (FSES), for a random
For 2014 GSS data on y = highest year of school completed, x1 = mother’s highest year of school completed, and x2 =father’s highest year of school completed, we obtain ˆy = 9.86 + 0.345x1 (r2 =
Refer to the previous exercise.(a) Report the F statistic for testing H0: β1 = β2 = 0, report its df values and P-value, and interpret.(b) Show how to construct the t statistic for testing H0:β1 =
Table 11.14 shows Stata output from fitting the multiple regression model to recent statewide data, excluding D.C., on y = violent crime rate (per 100,000 people), x1 = poverty rate (percentage with
For recentUNdata for several nations, a regression of carbon dioxide use (CO2, a measure of air pollution) on gross domestic product (GDP) has a correlation of 0.786.With life expectancy as a second
Recent UN data from several nations on y = crude birth rate (number of births per 1000 population size), x1 = women’s economic activity (female labor force as percentage of male), and x2 = GNP (per
Refer to the previous exercise. Using software with the Florida data file at the text website,(a) Construct box plots for each variable and scatterplots and partial regression plots between y and
The Florida data file, shown partly on page 283, has data from the 67 Florida counties on y = crime rate(number per 1000 residents), x1 = median income (thousands of dollars), and x2 = percentage in
Refer to the previous exercise.(a) Show how to obtain R-squared from the sums of squares in the ANOVA table. Interpret it.(b) r2 = 0.78 when GDP is the sole predictor. Why do you think R2 does not
A regression analysis with recent UN data from several nations on y = percentage of people who use the Internet, x1 = per capita gross domestic product (in thousands of dollars), and x2 = percentage
Use software with the Crime2 data file at the text website, with murder rate (number of murders per 100,000 people) as the response variable and with percentage of high school graduates and the
The Social Progress Index (see www.socialprogressimperative.org) is a measure of national progress in delivering social and environmental value.It is an average of three component measures: BHN
For recent data in Jacksonville, Florida, on y = selling price of home (in dollars), x1 =size of home (in square feet), and x2 = lot size (in square feet), the prediction equation is ˆy = −10,536
For students at Walden University, the relationship between y = college GPA (with range 0–4.0) and x1 =high school GPA (range 0–4.0) and x2 = verbal college board score (range 200–800)
4.44.* Refer to the previous exercise. Describe the sampling distribution of ¯y(a) for a random sample of size n = 1;(b) if you sample all 50,000 residents.
9.65.*Refer to the previous exercise. Let ρ1 and ρ2 denote the population correlation values between two variables for two separate populations. Let r1 and r2 denote sample values for independent
9.67.* The formula for the correlation can be expressed as(a) Using the first formula, explain why the correlation has the same value when x predicts y as when y predicts x.(b) By the second formula,
9.69.* Suppose that the linear regression model E(y) = α + βx with normality and constant standard deviation σ is truly appropriate. Then, the interval of numberspredicts where a new observation
In murder trials7 in 20 Florida counties in two years, the death penalty was given in 19 out of 151 cases in which a white killed a white, in 0 out of 9 cases in which a white killed a black, in 11
Consider the relationship between y = political party preference (Democrat, Republican) and x1 = race(Black, White) and x2 = gender. There is an association between y and both x1 and x2, with the
Example 9.10 (page 265) used a data set on house sales to regress y = selling price of home (in dollars) to x= size of house (in square feet). The prediction equation was ˆy = −50,926 + 126.6x.

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