Mean Mode Variance Standard deviation Descriptive statistics Least squares line
ID: 3068379 • Letter: M
Question
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.