Data for 4.139 Bone Age Loss 38 75 38 79 45 82 44 81 35 52 29 60 42 74 36 71 28
ID: 3068384 • Letter: D
Question
Data for 4.139Bone Age Loss 38 75 38 79 45 82 44 81 35 52 29 60 42 74 36 71 28 59 44 83 29 78 25 77 33 80 35 57 41 52 33 67 41 80 28 65 25 59 32 67 34 64 53 80 37 77 41 69 35 81 30 69 34 52 43 73 17 59 22 52 31 68 31 57 41 53 43 78 37 83 30 76 22 53 37 66 38 60 33 52 27 59 38 52 36 71 28 66 37 75 35 82 32 55 42 74 36 64 50 78 37 79 22 53 41 79 38 68 29 72 27 68 38 56 37 67 36 50 31 76 38 84 47 84 36 58 36 76 19 65 24 59 35 63 26 64 35 56 32 76 38 80 31 57 16 50 42 83 46 75 41 78 21 51 40 65 22 56 31 55 50 72 36 79 39 82 31 65 36 53 30 69 37 75 44 77 30 50 36 75 36 73 51 82 42 78 15 58 40 62 45 70 35 76 38 55 39 79 20 50 43 82 27 60 53 84 45 85 38 62 30 60 35 51 34 72 34 70 25 61 41 83 48 74 32 50 44 79 35 67 31 56 31 75 30 74 43 64 31 71 32 67 43 82 43 81 25 53 30 57 Bone Age Loss 38 75 38 79 45 82 44 81 35 52 29 60 42 74 36 71 28 59 44 83 29 78 25 77 33 80 35 57 41 52 33 67 41 80 28 65 25 59 32 67 34 64 53 80 37 77 41 69 35 81 30 69 34 52 43 73 17 59 22 52 31 68 31 57 41 53 43 78 37 83 30 76 22 53 37 66 38 60 33 52 27 59 38 52 36 71 28 66 37 75 35 82 32 55 42 74 36 64 50 78 37 79 22 53 41 79 38 68 29 72 27 68 38 56 37 67 36 50 31 76 38 84 47 84 36 58 36 76 19 65 24 59 35 63 26 64 35 56 32 76 38 80 31 57 16 50 42 83 46 75 41 78 21 51 40 65 22 56 31 55 50 72 36 79 39 82 31 65 36 53 30 69 37 75 44 77 30 50 36 75 36 73 51 82 42 78 15 58 40 62 45 70 35 76 38 55 39 79 20 50 43 82 27 60 53 84 45 85 38 62 30 60 35 51 34 72 34 70 25 61 41 83 48 74 32 50 44 79 35 67 31 56 31 75 30 74 43 64 31 71 32 67 43 82 43 81 25 53 30 57 Mean Mode Variance Standard deviation Descriptive statistics Least squares line 108 109 116 Correlation Coefficient of determination 133 HAPTER EXERCISES a. Determine the mean and median. b. Determine the variance and standard deviatien c. Briefly describe what you have learned from 139 Osteoporosis is a condition in which bone density decreases, often resulting in broken bones. Bone density usually peaks at age 30 and decreases thereafter. To understand more aboat the condition, a random sample of women aged 50 years and over was recruited. Each woman's bone density loss was recorded. a. Compute the mean and median of these data. b. Compute the standard deviation of the bone your statistical analysis. 4.141 Refer to Exercise 4.139. In addition to the Exercise 4 ition to the bn r was receruited. Each womans density losses, the ages of the women were ae recorded. Compute the coefficient of determinai and describe what this statistic tells you. 4.142 Refer to Exercise 4.140. Suppose that in additie density losses. c. Describe what you have learned from the to recording the coffee sales, the manager a recorded the average temperature (measured i degrees Fahrenheit) during the game. These dau together with the number of cups of coffee sll were recorded. a. Compute the coefficient of determination. b. Determine the coefficients of the least squares statistics 140 4 140 The temperature in December in Buffalo, New York, is often below 40 degrees Fahrenheit (4 degrees Celsius). Not surprisingly when the National Football League Buffalo Bills play at home in December, coffee is a popular item at the concession stand. The concession manager would like to acquire more information so that he can manage inventories more efficiently. The num ber of cups of coffee sold during 50 games played in December in Buffalo was recorded line. c. What have you learned from the statistics calculated in parts a and b about the relationship between the number of cupsof coffee sold and the temperature?
Explanation / Answer
(4.139) (a) Mean = 35.008, Median = 36
(b) Standard deviation = 7.6838
(c) We see that, on average, the bone density loss value is 36. There is no outlier values in the data set, because the mean and median values are almost equal. This means that the distribution of the data is symmetric. From the SD, we can say that, on average, the bone density loss value lies within 7 units of the mean value of bone density loss, that is, 36.
(4.141) Coefficient of determination = 0.3297
This statistic tells us that 32.97% variation in the dependent variable value (bone density loss) is explained by the linear regression between bone density loss and the age of women. This also tells us that if we had fitted a least squares linear regression line between the two variables, then the fit would have not been good.
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