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statistics alive

Questions and Answers of Statistics Alive

13.92 Logistic slope At the x value where the probability of success is some value p, the line drawn tangent to the logistic regression curve has slope bp11 - p2.a. Explain why the slope is b>4 when
13.94 Class data Refer to the data file your class created in Activity 3 in Chapter 1. For variables chosen by your instructor, fit a multiple regression model and conduct descriptive and inferential
13.91 Parabolic regression A regression formula that gives a parabolic shape instead of a straight line for the relationship between two variables is my = a + b1 x + b2 x2.a. Explain why this is a
13.90 Simpson’s paradox Let y = death rate and x = average age of residents, measured for each county in Louisiana and in Florida. Draw a hypothetical scatterplot, identifying points for each
13.89 Indicator for comparing two groups Chapter 10 presented methods for comparing means for two groups.Explain how it’s possible to perform a significance test of equality of two population means
13.88 R can’t go down The least squares prediction equation provides predicted values yn with the strongest possible correlation with y out of all possible prediction equations of that form. Based
13.87 Adjusted R2 When we use R2 for a random sample to estimate a population R2, it’s a bit biased. It tends to be a bit too large, especially when n is small. Some software also reports Adjusted
13.86 Logistic versus linear For binary response variables, one reason that logistic regression is usually preferred over straight-line regression is that a fixed change in x often has a smaller
13.85 Multicollinearity For the high school female athletes data file, regress the maximum bench press on weight and percent body fat.a. Show that the F test is statistically significant at the 0.05
13.84 Why an F test? When a model has a very large number of predictors, even when none of them truly have an effect in the population, one or two may look significant in t tests merely by random
13.83 Properties of R2 Using its definition in terms of SS values, explain why R2 = 1 only when all the residuals are 0, and R2 = 0 when each yn = y. Explain what this means in practical terms.
13.82 Lurking variable Give an example of three variables for which you expect b • 0 in the model my = a + bx1 but b1 = 0 in the model my = a + b1 x1 + b2 x2. (Hint: The effect of x1 could be
13.81 Scores for religion You want to include religious affiliation as a predictor in a regression model, using the categories Protestant, Catholic, Jewish, Other. You set up a variable x1 that
13.80 True or false: Slopes For data on y = college GPA, x1 = high school GPA, and x2 = average of mathematics and verbal entrance exam score, we get yn = 2.70 + 0.45x1 for simple regression and yn =
13.79 True or false: Regression For each of the following statements, indicate whether it is true or false. If false, explain why it is false. In regression analysis:a. The estimated coefficient of
13.78 True or false: R and R2 For each of the following statements, indicate whether it is true or false. If false, explain why it is false.a. R2 is always the same as the square of ordinary
13.77 Multiple choice: Regression effects Multiple regression is used to model y = college cumulative performance index(CPI) using x1 = high school grade and x2 = average monthly attendance
13.76 Multiple choice: Interpret indicator In the model my = a + b1 x1 + b2 x2, suppose that x1 is an indicator variable for smoking, equalling 1 for smokers and 0 for nonsmokers.a. We set x1 = 0 if
13.75 Multiple Choice: Interpret parameter If yn = 2.4 + 4x1 + 3x2 - 6x3, then controlling for x2 and x3, the change in the estimated mean of y when x1 is increased from 25 to 50a. equals 100.b.
13.74 Unemployment and GDP Refer to Exercise 13.67.When unemployment rate of a country is added as an additional predictor to the model already containing CO2 and percentage of population not using
13.73 Why regression? In 100–200 words, explain to someone who has never studied statistics the purpose of multiple regression and when you would use it to analyze a data set or investigate an
13.72 Student data Refer to the FL Student Survey data file on the book’s website. Using software, conduct a regression analysis using y = college GPA and predictors high school GPA and sports
13.71 Factors affecting first home purchase The table summarizes results of a logistic regression model for predictions about first home purchase by young married households.The response variable is
13.70 AIDS and AZT In a study (reported in the New York Times, February 15, 1991) on the effects of AZT in slowing the development of AIDS symptoms, 338 veterans whose immune systems were beginning
13.69 Horseshoe crabs and width A study of horseshoe crabs found a logistic regression equation for predicting the probability that a female crab had a male partner nesting nearby by using x = width
13.68 Education and gender in modeling income Consider the relationship between yn = annual income (in thousands of dollars) and x1 = number of years of education by x2 = gender. Many studies in the
13.67 GDP, CO2, and Internet Consider predicting the per capita GDP (gross domestic product, in thousands of dollars), of a country, using x1 = carbon dioxide emissions per capita (in metric tons)
13.66 Significant fertility prediction? Refer to the previous exercise.a. Show how to construct the F statistic for testing H0: b1 = b2 = 0 from the reported mean squares, report its P-value, and
13.65 Modeling fertility For the World Data for Fertility and Literacy data file on the book’s website, a MINITAB printout follows that shows fitting a multiple regression model for y = fertility,
13.64 Effect of poverty on crime Refer to the previous exercise.Now we add x3 = percentage of single-parent families to the model. The SPSS table below shows results.Without x3 in the model, poverty
13.63 Violent crime A MINITAB printout is provided from fitting the multiple regression model to U.S. crime data for the 50 states (excluding Washington, D.C.)on y = violent crime rate, x1 = poverty
13.62 Softball data Refer to the Softball data set on the book’s website. Regress the difference (DIFF) between the number of runs scored by that team and by the other team on the number of hits
13.61 Predicting body strength In Chapter 12, we analyzed strength data for a sample of female high school athletes.When we predict the maximum number of pounds the athlete can bench press using the
13.60 House prices This chapter has considered many aspects of regression analysis. Let’s consider several of them at once by using software with the House Selling Prices OR data file on the
13.58 Death penalty and race The three-dimensional contingency table shown is from a study of the effects of racial characteristics on whether individuals convicted of homicide receive the death
13.57 Graduation, gender, and race The U.S. Bureau of the Census lists college graduation numbers by race and gender.The table shows the data for graduating 25-year-olds.College graduation Group
13.56 Many predictors of voting Refer to the previous two exercises. When the explanatory variables are x1 = family income, x2 = number of years of education, and x3 = gender (1 = male, 0 = female),
13.55 Equally popular candidates Refer to the previous exercise.a. At which income level is the estimated probability of voting for the Republican candidate equal to 0.50?b. Over what region of
13.54 Voting and income A logistic regression model describes how the probability of voting for the Republican candidate in a presidential election depends on x, the voter’s total family income (in
13.53 Cancer prediction (continued) Refer to the previous exercise.For what values of the radius do you estimate that a female has a probability of (a) 0.50, (b) greater than 0.50, and (c) less than
13.52 Cancer prediction A breast cancer study at a city hospital in New York used logistic regression to predict the probability that a female has breast cancer. One explanatory variable was x =
13.51 Hall of Fame induction Baseball’s highest honor is election to the Hall of Fame. The history of the election process, however, has been filled with controversy and accusations of favoritism.
13.50 Income and credit cards Example 12 used logistic regression to estimate the probability of having a travel credit card when x = annual income (in thousands of euros).Show that the estimated
13.49 Comparing revenue An entrepreneur owns two filling stations—one at an inner city location and the other at an interstate exit location. He wants to compare the regressions of y = total daily
13.48 Equal slopes for car prices? Refer to Exercise 13.41, with yn = predicted selling price of used car and x1 = age of car. When equations are fitted separately for U.S. and foreign cars, we get
13.47 House size and garage interact? Refer to the previous exercise.a. Explain what the no interaction assumption means for this model.b. Sketch a hypothetical scatter diagram, showing points
13.46 Houses, size, and garage Use the House Selling Prices OR data file on the book’s website to regress selling price in thousands on house size and whether the house has a garage.a. Report the
13.45 Predicting pizza sales A chain restaurant that specializes in selling pizza wants to analyze how y = sales for a customer (the total amount spent by a customer on food and beverage, in pounds)
13.44 Quality and productivity The table shows data from 27 automotive plants on y = number of assembly defects per 100 cars and x = time (in hours) to assemble each vehicle.The data are in the
13.43 Predict using house size and condition For the House Selling Prices OR data set, when we regress y = selling price (in thousands) on x1 = house size and x2 = condition (1 = Good, 0 = Not Good),
13.42 Mountain bike prices The Mountain Bike data file on the book’s website shows selling prices for mountains bikes. When y = mountain bike price($) is regressed on x1 = weight of bike (lbs) and
13.41 U.S. and foreign used cars Refer to the used car data file from Exercise 13.11. The prediction equation relating y = selling price of used car (in $) as a function of x1 = age of car and x2 =
13.40 Selling prices level off In the previous exercise, suppose house selling price tends to increase with a straight-line trend for small to medium size lots, but then levels off as lot size gets
13.39 House prices Use software with the House Selling Prices OR data file on the book’s website to do residual analyses with the multiple regression model for y = house selling price (in
13.38 College athletes The College Athletes data set on the book’s website comes from a study of University of Georgia female athletes. Using the column names from the data set, the response
13.37 Why inspect residuals? When we use multiple regression, what is the purpose of performing a residual analysis?Why is it better to work with standardized residuals than unstandardized residuals
13.36 Population growth with time Suppose you fit a straightline regression model to x = time and y = population.Sketch what you would expect to observe for (a) the scatterplot of x and y and (b) a
13.35 Nonlinear effects of age Suppose you fit a straight-line regression model to y = number of hours worked (excluding time spent on household chores) and x = age of the subject. Values of y in the
13.34 More residuals for strength Refer to the previous exercise.The following figure is a residual plot for the model relating maximum bench press to LP200 and BP60. It plots the standardized
13.33 Strength residuals In Chapter 12, we analyzed strength data for a sample of female high school athletes. The following figure is a residual plot for the multiple regression model relating the
13.32 Body weight residuals Examples 4–7 used multiple regression to predict total body weight of college athletes in terms of height, percent body fat, and age. The following figure shows a
13.31 House prices Use software to do further analyses with the multiple regression model of y = selling price of home in thousands, x1 = size of home, and x2 = number of bedrooms, considered in
13.30 More predictors for selling price The MINITAB results are shown for predicting selling price using x1 = size of home, x2 = number of bedrooms, and x3 = age.a. State the null hypothesis for an F
13.29 Gain in human development Refer to the previous exercise.a. Report the test statistic and P-value for testing H0: b1 = b2 = 0.b. State the alternative hypothesis that is supported by the result
13.28 Regression for human development A study investigated an index of human development in a South American country, which had y = 27.3 and s = 5.5. Two explanatory variables were x1 = literacy
13.27 Predicting restaurant revenue An Italian restaurant keeps monthly records of its total revenue, expenditure on advertising, prices of its own menu items, and the prices of its
13.26 Any predictive power? Refer to the previous three exercises.a. State and interpret the null hypothesis tested with the F statistic in the ANOVA table given in Exercise 13.23.b. From the F table
13.25 Interpret strength variability Refer to the previous two exercises.The sample standard deviation of maxBP was 13.3.The residual standard deviation of maxBP when BP60 and LP200 are predictors in
13.24 Leg press uncorrelated with strength? The P-value of 0.17 in part a of the previous exercise suggests that LP200 plausibly had no effect on maxBP once BP60 is in the model. Yet when LP200 is
13.23 Does leg press help predict body strength?Chapter 12 analyzed strength data for 57 female high school athletes. Upper body strength was summarized by the maximum number of pounds the athlete
13.22 Variability in college CPI Refer to the previous two exercises.a. Report the residual standard deviation. What does this describe?b. Interpret the residual standard deviation by predicting
13.21 Study time helps CPI? Refer to the previous exercise.a. Report and interpret the P-value for testing the hypothesis that the population slope coefficient for study time equals 0.b. Find a 95%
13.20 Predicting CPI For a random sample of 100 students in a German university, the result of regressing the college cumulative performance index (CPI) on the high school grade (HSG), the average
13.19 Predicting college GPA Using software with the Georgia Student Survey data file from the book’s website, find and interpret the multiple correlation and R2 for the relationship between y =
13.18 Slopes, correlations, and units In Example 2 on y = house selling price, x1 = house size, and x2 = number of bedrooms, yn = 60,102 + 63.0x1 +15,170x2, and R = 0.72.a. Interpret the value of the
13.17 Softball data For the Softball data set on the book’s website, for each game, the variables are a team’s number of runs scored (RUNS), number of hits (HIT), number of errors (ERR), and the
13.16 Price, age, and horsepower In the previous exercise, r2 = 0.66 when age is the predictor and R2 = 0.69 when both age and HP are predictors. Why do you think that the predictions of price
13.15 Price of used cars For the 19 used cars listed in the Used Cars data file on the book’s website (see also Exercise 13.11), modeling the mean of y = used car price in terms of x1 = age results
13.14 When does controlling have little effect? Refer to the previous exercise. Height has a similar estimated slope for each of the three models. Why do you think that controlling for % body fat and
13.13 Predicting weight Let’s use multiple regression to predict total body weight (TBW, in pounds) using data from a study of female college athletes. Possible predictors are HGT = height (in
13.12 Predicting average monthly visitor satisfaction Refer to Exercise 13.3 about the multiple linear regression of a restaurant’s average monthly visitor satisfaction rating (y) on the monthly
13.11 Used cars The following data (also available from the book’s website) is from a random sample of campus newspaper ads on used cars for sale. Consider the age and horsepower (HP) of a car to
13.10 House selling prices Using software with the House Selling Prices OR data file on the book’s website, analyze y = selling price, x1 = house size, and x2 = lot size.a. Construct box plots for
13.9 Controlling has an effect The slope of x1 is not the same for multiple linear regression of y on x1 and x2 as compared to simple linear regression of y on x1, where x1 is the only predictor.
13.8 Comparable number of bedrooms and house size effects In Example 2, the prediction equation between y = selling price and x1 = house size and x2 = number of bedrooms was yn = 60,102 + 63.0x1 +
13.7 The economics of golf The earnings of a PGA Tour golfer are determined by performance in tournaments.A study analyzed tour data to determine the financial return for certain skills of
13.6 Crime rate and income Refer to the previous exercise.MINITAB reports the following results for the multiple regression of y = crime rate on x1 = median income(in thousands of dollars) and x2 =
13.5 Does more education cause more crime? The FL Crime data file on the book’s website has data for the 67 counties in Florida on y = crime rate: Annual number of crimes in county per 1000
13.4 Interpreting slopes on average monthly visitor satisfaction Refer to the previous exercise.a. Explain why setting x2 at a variety of values yields a collection of parallel lines relating yn to
13.3 Predicting visitor satisfaction For all the restaurants in a city, the prediction equation for y = average monthly visitor satisfaction rating (range 0–4.0 where 0 =very poor and 4 = very
13.2 Does study help GPA? For the Georgia Student Survey file on the book’s website, the prediction equation relating y = college GPA to x1 = high school GPA and x2 = study time (hours per day), is
13.1 Predicting weight For a study of female college athletes, the prediction equation relating y = total body weight (in pounds) to x1 = height (in inches) and x2 = percent body fat is yn = -121 +
12.107 Analyze your data Refer to the data file you created in Activity 3 at the end of Chapter 1. For variables chosen by your instructor, conduct a regression and correlation analysis. Report both
12.106 Rule of 72 You invest $1000 at 6% compound interest a year. How long does it take until your investment is worth $2000?a. Based on what you know about exponential regression, explain why the
12.105 Regression with an error term4 An alternative to the regression formula my = a + bx expresses each y value, rather than the mean of the y values, in terms of x. This approach models an
12.104 Standard error of slope The formula for the standard error of the sample slope b is se = s>Σ1x - x22, where s is the residual standard deviation.a. Show that the smaller the value of s, the
12.103 r2 and variances Suppose r2 = 0.30. Since Σ1y - yQ 22 is used in estimating the overall variability of the y values and Σ1y - yn22 is used in estimating the residual variability at any fixed
12.102 Why is there regression toward the mean? Refer to the relationship r = 1sx>sy2b between the slope and correlation, which is equivalently sxb = rsy.a. Explain why an increase in x of sx units
12.101 Golf club velocity and distance A study about the effect of the swing on putting in golf (by C. M. Craig et al., Nature, vol. 405, 2000, pp. 295–296) showed a very strong linear relationship
12.100 True or false The variables y = annual income (thousands of dollars), x1 = number of years of education, and x2 = number of years experience in job are measured for all the employees having

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