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essentials of statistics
Essentials Of Statistics For The Behavioral Sciences 5th Edition Susan A. Nolan, Thomas Heinzen - Solutions
14.48 The age of a country, the level of concern for the environment, and multiple regression: Researchers analyzed the impact of the age of a country on the overall level of concern for the environment (Hershfield et al., 2014). They noted that some countries—Sweden, for example—are more
14.47 Sugar, diabetes, and multiple regression: A New York Times reporter wrote: “A study published in the journal PLOS ONE links increased consumption of sugar with increased rates of diabetes by examining the data on sugar availability and the rate of diabetes in 175 countries over the past
14.46 Google, the flu, and third variables: The New York Times reported: “Several years ago, Google, aware of how many of us were sneezing and coughing, created a fancy equation on its Web site to figure out just how many people had influenza. The math works like this: people’s location +
14.45 Cohabitation, divorce, and prediction: A study by the Institute for Fiscal Studies (Goodman & Greaves, 2010) found that parents’ marital status when a child was born predicted the likelihood of the relationship’s demise. Parents who were cohabitating when their child was born had a 27%
14.44 Anxiety, depression, and multiple regression: We conducted a second regression analysis on the data from the previous exercise. In addition to depression at year 1, we included a second predictor variable to predict anxiety at year 3. We also included anxiety at year 1. (We might expect that
14.43 Anxiety, depression, and simple linear regression: We analyzed data from a larger data set that one of the authors used for previous research (Nolan et al., 2003). In the current analyses, we used regression to look at factors that predict anxiety over a 3-year period. Shown below is the
14.42 Tutoring, mathematics performance, and problems with regression: A researcher conducted a study in which children with problems learning mathematics were offered the opportunity to purchase time with special tutors. The number of weeks that children met with their tutors varied from 1 to 20.
14.41 Cola consumption, bone mineral density, and limitations of regression: Does one’s cola consumption predict one’s bone mineral density? Using regression analyses, nutrition researchers found that older women who drank more cola (but not more of other carbonated drinks) tended to have lower
14.40 Precipitation, violence, and limitations of regression: Does the level of precipitation predict violence? Dubner and Levitt (2006b) reported on various studies that found links between rain and violence. They mentioned one study by Miguel, Satyanath, and Sergenti that found that decreased
14.39 Hours studied, grade, and regression: A regression analysis of data from some of our statistics classes yielded the following regression equation for the predictor variable (hours studied) and the outcome variable (grade-point average [GPA]): Yˆ = 2.96 + 0.02(X).a. If you plan to study 8
14.37 Consideration of Future Consequences scale, z scores, and raw scores: A study of Consideration of Future Consequences (CFC) found a mean score of 3.51, with a standard deviation of 0.61, for the 664 students in the sample (Petrocelli, 2003).a. Imagine that your z score on the CFC score was
14.36 Age, hours studied, and prediction: In How It Works 13.2, we calculated the correlation coefficient between students’ age and number of hours they study per week. The correlation between these two variables is 0.49.a. Elifs z score for age is −0.82. What would we predict for the z score
14.35 Predictive policing: The New York Times reported on predictive policing, a strategy based on formulas that “forecast” whether a particular person is likely to commit a crime (Elgion & Williams, 2015). What are the predictive data that the police consider? They look at personal
14.34 Birth weight, blood pressure, and regression: A metaanalysis found a negative correlation between birth weight and blood pressure later in life (Mu et al., 2012).a. Explain what is meant by a negative correlation between these two variables.b. If you were to examine these two variables with
14.33 Use this output from a multiple regression analysis to answer the following questions:a. Write the equation for the line of prediction.b. Use the equation for part (a) to make predictions for: SAT = 1030, rank = 41.c. Use the equation for part (a) to make predictions for: SAT = 860, rank =
14.32 Use this output from a multiple regression analysis to answer the following questions:a. Write the equation for the line of prediction.b. Use the equation for part (a) to make predictions for: variable 1 = 6, variable 2 = 60.c. Use the equation for part (a) to make predictions for: variable 1
14.31 Data are provided here with descriptive statistics, a correlation coefficient, and a regression equation: r = 0.52, Yˆ = 2.643 + 0.469(X).X Y 4.00 6.00 6.00 3.00 7.00 7.00 8.00 5.00 9.00 4.00 10.00 12.00 12.00 9.00 14.00 8.00 MX = 8.75 MY = 6.75 SDX = 3.031 SDY = 2.727 Using this
14.30 Data are provided here with descriptive statistics, a correlation coefficient, and a regression equation: r = 0.426, Yˆ = 219.974 + 186.595(X). X Y 0.13 200.00 0.27 98.00 0.49 543.00 0.57 385.00 0.84 420.00 1.12 312.00 MX = 0.57 MY = 326.333 SDX = 0.333 SDY = 145.752 Using this information,
14.29 Given the regression line Yˆ = 49 − 0.18(X), make predictions for each of the following:a. X =−31b. X = 65c. X = 14
14.28 Given the regression line Yˆ =−6 + 0.41(X), make predictions for each of the following:a. X = 25b. X = 50c. X = 75
14.27 Let’s assume we know that age is related to bone density, with a Pearson correlation coefficient of −0.19. (Notice that the correlation is negative, indicating that bone density tends to be lower at older ages than at younger ages.) Assume we also know the following descriptive
14.26 Using the following information, make a prediction for Y, given an X score of 8: Variable X: M = 12, SD = 3 Variable Y: M = 74, SD = 18 Pearson correlation of variables X and Y = 0.46a. Transform the raw score for the predictor variable into a z score.b. Calculate the predicted z score for
14.25 Using the following information, make a prediction for Y, given an X score of 2.9: Variable X: M = 1.9, SD = 0.6 Variable Y: M = 10, SD = 3.2 Pearson correlation of variables X and Y = 0.31a. Transform the raw score for the predictor variable into a z score.b. Calculate the predicted z score
14.24 What are some of the ethical issues associated with using regression to predict individuals’ future behavior?
14.23 In what ways have regression tools been used to predict individuals’ future behavior?
14.22 What is the difference between the symbol for the effect size for simple linear regression and the symbol for the effect size for multiple regression?
14.21 Why is multiple regression often more useful than simple linear regression?
14.20 If you know the correlation coefficient, how can you determine the proportionate reduction in error?
14.19 What is an orthogonal variable?
14.18 What information does the proportionate reduction in error give us?
14.17 What are the basic steps to calculate the proportionate reduction in error?
14.16 When drawing error lines between data points and the regression line, why is it important that these lines be perfectly vertical?
14.15 What is SStotal?
14.14 Explain why the regression equation is a better source of predictions than the mean.
14.13 What is the connection between regression to the mean and the bell-shaped normal curve?
14.12 Why are explanations of the causes behind relations explored with regression limited in the same way they are with correlation?
14.11 What is the difference between a small standard error of the estimate and a large one?
14.10 How are the sign of the correlation coefficient and the sign of the slope related?
14.9 Why do we also call the regression line the line of best fit?
14.8 What does the slope tell us?
14.7 When is the intercept not meaningful or useful?
14.6 What are the three steps to calculate the intercept?
14.5 The equation for a line is Yˆ = a + b(X). Define the symbols a and b.
14.4 What does each of the symbols stand for in the formula for the regression equation: z Yˆ = (rXY )(zX)?
14.3 Is there any difference between Yˆ and a predicted score for Y? Explain your answer.
14.2 How does the regression line relate to the correlation of two variables?
14.1 What does regression add above and beyond what we learn from correlation?
13.55 High school athletic participation and correlation: Researchers examined longitudinal data to explore the long-term effects of high school athletic participation in the United States (Lutz et al., 2009). They reported three findings. First, they found that high school athletic participation
13.54 Availability of food, amount eaten, and correlation: Did you know that sometimes you eat more just because the food is in front of you? Geier et al., (2006) studied how portion size affected the amount people consumed. They discovered interesting things such as that people eat more M&M’s
13.53 Health care spending, longevity, and correlation: The New York Times columnist Paul Krugman (2006) used the idea of correlation in a newspaper column when he asked, “Is being an American bad for your health?” Krugman explained that the United States has higher per capita spending on
13.52 Divorce rate, margarine consumption, and big data: Using data from the National Vital Statistics Reports and the U.S. Department of Agriculture, Tyler Vigen (2015) demonstrated a strong correlation of r = 0.99 between the divorce rate in Maine and the per capita consumption of margarine in
13.51 Flu epidemics and correlation: In 2009, researchers at Google demonstrated that they could detect the spread of flu epidemics in the United States based on the correlation between a set of Google search terms that users were entering and the number of doctor’s visits for the flu (Ginsberg
13.50 Psychologists, housewives of New Jersey, and a spurious correlation: An online tool, Google Correlate (which shut down in 2019), reported a correlation in regional Google searches in the United States between the word “psychologist” and the phrase “housewives of New Jersey season 4,”
13.49 Swearing, vocabulary, and correlation: Psychology researchers set out to test the folk assumption that people swear a lot because their overall vocabulary is limited (Jay & Jay, 2015). They asked participants to name as many taboo words, described as “curse words or swear words” (p. 253),
13.47 Correlation versus causation, iPhones, and millennials: One newspaper headline, noting that 18- to 34-year-olds were increasingly likely to move back home following the 2007 release of the iPhone, asked: “Did the Release of the iPhone Cause Millennials to Move Back in with Their Parents?”
13.46 Correlation versus causation and hate crimes: Using municipalities (i.e., towns, cities) in Germany as participants, researchers found an association between the numbers of anti-refugee posts on social media and the numbers of violent acts against refugees (Müller & Schwarz, 2018). (Note
13.45 Arts education, correlation, and causality: The Broadway musical Annie and the Entertainment Industry Foundation teamed up to promote arts education programs for underserved children. In an ad in The New York Times, they said, “Students in arts education programs perform better and stay in
13.44 Standardized tests, correlation, and causality: A New York Times editorial (“Public vs. Private Schools,” 2006) cited a finding by the U.S. Department of Education that standardized test scores were significantly higher among students in private schools than among students in public
13.43 Driving a convertible, correlation, and causality: How safe are convertibles? USA Today (Healey, 2006) examined the pros and cons of convertible automobiles. The Insurance Institute for Highway Safety determined that, depending on the model, 52 to 99 drivers of 1 million registered
13.42 IQ-boosting water and illusory correlation: The trashy tabloid Weekly World News published an article—“Water from Mountain Falls Can Make You a Genius”—stating that drinking water from a special waterfall in a secret location in Switzerland “boosts IQ by 14 points—in the blink of
13.41 Traffic, running late, and bias: A friend tells you that there is a correlation between how late she’s running and the amount of traffic. Whenever she’s going somewhere and she’s behind schedule, there’s a lot of traffic. And when she has plenty of time, the traffic is sparser. She
13.40 Trauma, masculinity, and hypothesis testing for correlation: Using the data and your work in the previous exercise, perform the remaining five steps of hypothesis testing to explore the relation between trauma and masculinity. In Step 6, be sure to evaluate the size of the correlation using
13.39 Trauma, masculinity, and correlation: See the description of Holiday’s experiment in Exercise 13.37. We calculated the correlation coefficient for the relation between the perception of a situation as traumatic and the perception of a woman’s femininity. Now let’s look at data to
13.38 Trauma, femininity, and hypothesis testing for correlation: Using the data and your work in the previous exercise, perform the remaining five steps of hypothesis testing to explore the relation between trauma and femininity. In Step 6, be sure to evaluate the size of the correlation using
13.37 Trauma, femininity, and correlation: Graduate student Angela Holiday (2007) conducted a study examining perceptions of combat veterans suffering from mental illness. Participants read a description of either a male or female soldier who had recently returned from combat in Iraq and who was
13.36 Cats, mental health problems, and scatterplots: Consider the scenario in the previous exercise again. The two variables under consideration were (1) number of cats owned and (2) level of mental health problems (with a higher score indicating more problems). Each possible relation between
13.35 Cats, mental health problems, and the direction of a correlation: You may be aware of the stereotype about the “crazy” person who owns a lot of cats. Have you wondered whether the stereotype is true? As a researcher, you decide to assess 100 people on two variables: (1) the number of cats
13.34 Direction of a correlation: For each of the following pairs of variables, would you expect a positive correlation or a negative correlation between the two variables? Explain your answer.a. How hard the rain is falling and your commuting timeb. How often you say no to dessert and your body
13.33 Externalizing behavior, anxiety, and hypothesis testing for correlation: Using the data in the previous exercise, perform all six steps of hypothesis testing to explore the relation between externalizing and anxiety.
13.32 Externalizing behavior, anxiety, and correlation: As part of their study on the relation between rejection and depression in adolescents (Nolan et al., 2003), researchers collected data on externalizing behaviors (e.g., acting out in negative ways, such as causing fights) and anxiety. They
13.31 Exercise, number of friends, and correlation: Does the amount that people exercise correlate with the number of friends they have? The accompanying table contains data collected in some of our statistics classes. The first and third columns show hours exercised per week and the second and
13.30 Obesity, age at death, and correlation: In a newspaper column, Paul Krugman (2006) mentioned obesity (as measured by body mass index) as a possible correlate of age at death.a. Describe the implied correlation between these two variables. Is it likely to be positive or negative? Explain.b.
13.29 Debunking astrology with correlation: The New York Times reported that an officer of the International Society for Astrological Research, Anne Massey, stated that a certain phase of the planet Mercury, the retrograde phase, leads to breakdowns in areas as wide-ranging as communication and
13.28 Awe and correlation in the news: The New York Times reported on a study that examined the link between positive emotions and health. First citing previous research connecting negative moods with poor health, the reporter said: “Far less is known, however, about the health benefits of
13.27 Grip strength, mortality, and correlation: An international team of researchers studied the association between grip strength (using a tool that measures the strength of participants’ hands) and mortality among adults in 17 countries (Leong et al., 2015). They reported that “Low grip
13.26 Quick thinking, smooth talking, and a correlation: Australian psychologist William von Hippel and his colleagues examined the premise that the ability to think quickly would be related to social skills in a paper titled “Quick Thinkers Are Smooth Talkers” (von Hippel et al., 2016). They
13.25 Calculate the degrees of freedom and the critical values, or cutoffs, assuming a two-tailed test with an alpha level of 0.05, for each of the following designs:a. Data are collected to examine the relation between size of dog and rate of bone and joint health issues. Veterinarians from around
13.24 Calculate the degrees of freedom and the critical values, or cutoffs, assuming a two-tailed test with an alpha level of 0.05, for each of the following designs:a. Forty students were recruited for a study about the relation between knowledge regarding academic integrity and values held by
13.23 Using the following data:X Y 40 60 45 55 20 30 75 25 15 20 35 40 65 30a. Create a scatterplot.b. Calculate deviation scores and products of the deviations for each individual, and then sum all products. This is the numerator of the correlation coefficient equation.c. Calculate the sum of
13.22 Using the following data:X Y 394 25 972 75 349 25 349 65 593 35 276 40 254 45 156 20 248 75a. Create a scatterplot.b. Calculate deviation scores and products of the deviations for each individual, and then sum all products. This is the numerator of the correlation coefficient equation.c.
13.21 Using the following data:X Y 0.13 645 0.27 486 0.49 435 0.57 689 0.84 137 0.64 167a. Create a scatterplot.b. Calculate deviation scores and products of the deviations for each individual, and then sum all products. This is the numerator of the correlation coefficient equation.c. Calculate the
13.20 For each of the pairs of correlation coefficients provided, determine which one indicates a stronger relation between variables:a. −0.28 and −0.31b. 0.79 and 0.61c. 1.0 and −1.0d. −0.15 and 0.13
13.19 Use Cohen’s guidelines to describe the strength of the following correlation coefficients:a. −0.28b. 0.79c. 1.0d. −0.015
13.18 Decide which of the three correlation coefficient values below goes with each of the scatterplots presented in the previous exercise.a. 0.545b. 0.018c. −0.20
13.17 Determine whether the data in each of the graphs provided would result in a negative or positive correlation coefficient.
13.16 What is the relation between big data and spurious correlations?
13.15 What is the big data approach?
13.14 Describe the third assumption of hypothesis testing with correlation.
13.13 What are the three basic steps to calculate the Pearson correlation coefficient?
13.12 What are the null and research hypotheses for correlations?
13.11 What is meant by a spurious correlation, and why might it be a Type I error?
13.10 Why can we not infer causation from correlation?
13.9 Explain how the sum of the product of deviations determines the sign of the correlation.
13.8 How are deviation scores used in assessing the relation between variables?
13.7 Explain how the correlation coefficient can be used as a descriptive statistic or an inferential statistic.
13.6 When we have a straight-line relation between two variables, we use a Pearson correlation coefficient. What does this coefficient describe?
13.5 What magnitude of a correlation coefficient is large enough to be considered important, or worth talking about?
13.4 What is the difference between a positive correlation and a negative correlation?
13.3 Describe a perfect correlation, including its possible coefficients.
13.2 What is a linear relation?
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