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How strong is the relationship? 0 Not strong at all 0 moderately strong 0 very strong (c) Now add the data for the male subjects to your graphr using a different color or a different plotting symbol. (Do this on paper. Your instructor may ask you to turn in this graph.) Does the pattern of relationship that you observed in (b) hold for men also? 0 Yes 0N0 How do the male subjects as a group differ From the female subjects as a group? O The males typically have larger values for both lean body mass and metabolic rate. 0 There are No specific patterns. 0 The females typically have larger values for both lean body mass and metabolic rate. 0 Males and females have the same values for both lean body mass and metabolic rate. Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. The following table gives data on the lean body mass and resting metabolic rate for 12 women and 7 men who are subjects in a study of dieting. Lean body mass, give in kilograms, is a person's weight leaving out all fat. Metabolic rate is measured in colories burned per 24 hours, the same calories used to describe the energy content of foods. The researchers believe that lean body mass is an important influence on metabolic rate. TABLE 3.2 Lean body mass and metabolic rate Subject Sex Mass (kg) Rate (cal) Subject Sex Mass (kg) Rate (cal) M 62.0 1792 11 F 40.3 1189 M 62.9 1666 12 F 33.1 913 F 36.1 995 13 M 51.9 1460 54.6 1425 14 F 42.4 1124 48.5 1396 15 F 34.5 1052 42.0 1418 16 F 51.1 1347 M 47.4 1362 17 F 41.2 1204 50.6 1502 18 M 51.9 1867 42.0 1256 19 M 46.9 1439 M 48.7 1614 (a) Make a scatterplot of the data for the female subjects. (Do this on paper. Your instructor may ask you to turn in this graph.) Which is the explanatory variable? O metabolic rate O subject O gender O body mass (b) Is the association between these variables positive or negative? O positive O negative What is the form of the relationship? O linear O Nonlinear O undeterminedProfessor Moore swims 2000 yards regularly in a vain attempt to undo middle age. Here are his times (in minutes} and his pulse rate after swimming (in beats per minutes) for 23 sessions in the pool. Time: 34.12 35.72 34.72 34.05 34.13 35.72 36.17 35.57 35.37 Pulse: 152 124 140 152 146 128 136 144 1.48 Time: 35.57 35.43 36.05 34.85 34.70 34.75 33.93 34.60 34.00 Pulse: 144 136 124 148 144 140 156 136 1.48 Time: 34.35 35.62 35.68 35.20 35.97 Pulse: 148 132 124 132 139 (a) Make a scatterplot. (Do this on paper. Your instructor may ask you to turn in this graph.) which is the explanatory variable?J 0 time 0 pulse (b) [s the association between these variables positive or negative? 0 positive 0 negative Explain why you expect the relationship to have this direction. 0 Swimming faster requires greater effort and hence it would lower the pulse rate. 0 Swimming taster requires less effort and hence it would raise the pulse rate higher. 0 Swimming taster requires less effort and hence it would lower the pulse rate. 0 Swimming taster requires greater effort and hence it would raise the pulse rate higher. (c) Describe the form and strength of the relationship. 0 This is a weakly linear relationship. 0 This is a moderately linear relationship. 0 This is a strong linear relationship. 0 This is a nonlinear relationship. The following table gives the lengths of two bones in ve fossil specimens of the extinct beast Archaeopteryx. Femur: 38 56 59 64 F'4 Humerus: 41 63 F'O Y2 84 The correlation, r, between these two variables is 0.994. (a) Make a scatterplot. [Do this on paper. Your instructor mayr ask you to turn in this graph.) Explain why the value of r matches the scatterplot. O The plot shows a strong positive linear relationship, with little scatter, so we expect that r is close to 1. O The plot shows a strong negative linear relationship, with little scatter, so we expect that r is close to 1. O The plot shows a strong positive linear relationship, with little scatter, so we expect that r is close to 1. O The plot shows a weak positive linear relationship, with little scatter, so we expect that r is close to 0. (b) The lengths were measured in centimeters. If we changed to inches, how would r change? [There are 2.54 centimeters in an inch.) 0 The value of r would increase. 0 We would not be able to determine the change of r. O The value of r would not change. 0 The value of r would decrease. The gas mileage of an automobile first increases and then decreases as the speed increases. Suppose that this relationship is very regular, as shown by the following data on speed (miles per hour) and mileage (miles per gallon). Speed: 20 30 40 50 60 MPG: 24 28 30 28 24 Make a scatterplot of mileage versus speed. Show that the correlation between speed and mileage is r = 0. (Do this on paper. Your instructor may ask you to turn in this graph.) Explain why the correlation is 0 even though there is a strong relationship between speed and mileage. O Correlation only measures linear relationships; this plot shows a non-linear relationship. O We only have 5 observations--it is not sufficient to determine the true correlation. O The distribution is symmetric. O One section shows a positive linear relationship and the other section shows a negative relationship, they cancel each other out.A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, "The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero." The paper repons this as: "Professor McDaniel said that good researchers tend to be poor teachers, and vice versa." Explain why the paper's report is wrong. 0 The person who wrote the article interpreted a correlation close to 0 as if it were a correlation close to 0.1. O The person who wrote the article interpreted a correlation close to 0 as if it were a correlation close to 1. O The person who wrote the article interpreted a correlation close to 0 as if it were a correlation close to 71. O The person who wrote the article interpreted a correlation close to 0 as if it were a correlation close to -O.l. Select a statement in plain language (don't use the word "correlation") to explain the psychologists meaning. 0 Professor McDaniel's ndings mean there is nonrlinear association between research and teaching. 0 Professor McDaniel's ndings mean there is little linear association between research and teaching. 0 Professor McDaniel's findings mean there is very strong linear association between research and teaching. 0 Professor McDaniel's findings mean there is moderately strong linear association between research and teaching. Each of the following statements contains a blunder. Explain in each case what is wrong. (a) "There is a high correlation between the gender of American workers and their income." 0' Income is a categorical variable. 0 Gender is a quantitative variable. 0 Income is a quantitative variable. 0 Gender is a categorical variable. 0 There is nothing wrong with the statement. (b) "We found a high correlation (r = 1.09) between students' ratings of faculty teaching and ratings made by other faculty members. 0 r = 1.09 is too small. 0 rmust be an integer. O r can not be positive. 0 There is nothing wrong with the statement. 0 r must be between 1 and 1. (c) "The correlation between planting rate and yield of corn was found to be r = 0.23 bushel." 0 There is nothing wrong with the statement. 0 ris positive. 0 r is too small. 0' r is too big. 0 r should be unitless. A study of class attendance and grades among first-year students at a state university showed that in general students who attended a higher percent of their classes earned higher grades. Class attendance explained 20% of the variation in grade index among the students. What is the numerical value of the correlation between percent of classes attended and grade index? 1 =Some people think that the behavior of the stock market In January predicts Its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for the entire year. We expect a positive correlation between x and y because the change during January contributes to the full yeai's change. Calculation from data for the years 1960 to 1997 gives ; : 1.75% 5x = 5 33% r : 0.597 ,7 = 9.05% sy : 15.36% (a) What percent of the observed variation In yearly changes In the index is explained by a straightrline relationship With the change during January? (Round your answer to one decimal place.) (b) What is the equation of the least-squares line for prediction full-year change from January change? (Round your answers to three decimal places.) 9 : :l + :lx (c) The mean change in January is ; = 1.75%. Use your regression line to predict the change In the index In a year in which the index rises 1.75% in January. (Round your answer to two decimal plaoes.) Why could you have given this result (up to roundoi'f error) without doing the calculation? 0 The regression line must pass through (5)\" 5y) 0 Tthe {lavalue is moderately high. 0 The regression line must pass through (0,0). 0 The regression line must pass through (;, )7). The following figure plots school grade point average (GPA) against IQ test score for 78 seventh-grade students. 12- 10 Grade point average 60 65 70 75 80 85 90 95 100105 110 115 120 125 130135 140 IQ score Calculation shows that the mean and standard deviation of the IQ scores are x = 108.4 5x = 13.15 For the grade point averages, y = 7.443 5y = 2.17 The correlation between 1Q and GPA is r = 0.6334. (a) Find the equation of the least-squares line for prediction GPA from IQ. y = X (b) What percent of the observed variation in these students' GPAs can be explained by the linear relationship between GPA and IQ? (c) One student has an 1Q of 104 but a very low GPA of 0.56. What is the predicted GPA for a student with IQ = 104? What is the residual for this particular student