4. (35 points, 5 points each).  A random sample of patients yields the following results for the dosage of an experimental drug (X) and the patients symptom level (Y). Dosage (X)                          0              0              0              10           10           20           20           30           30 Symptom Level (Y)           80           95           70           68           56           42           32           50           28 b. What is the sample correlation?  Is it strong, weak, or moderate? c. What is the equation for the regression line? d. What proportion of the variation in y can be explained by its linear relationship with x? e. Predict the symptom level when the dosage is 50. f. Predict the symptom level when the dosage is 15. g. List three points on the regression line. h. Can we conclude that an increase in the dosage level causes a decrease in symptom level?  Why or why not?

For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy

Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?

Noise and Intelligibility Audiologists study the intelligibility of spoken sentences under different noise levels. Intelligibility, the MRT score, is measured as the percent of a spoken sentence that the listener can decipher at a cesl4ain noise level in decibels (dB). The table shows the results of one such test. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Find the correlation coefficient. Is a linear model appropriate? (d) Use the linear model in put (b) to estimate the intelligibility of a sentence at a 94-dB noise level.

For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.

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If a correlation isr= 0.00, then SP = 0 and the regression equation is O Ý =X +0 O Ý =X + X O Ý =0 + X O Ý =Ÿ + 0

A football coach is looking for a way to identify players that are "under weight". The coach decides to get data for each player's height (x, in inches) and weight (y, in pounds), then does a linear regression. The results are: y = - 52 + 3x,r = 0.9 and the standard error is Se = 10.4. Since there is a strong linear correlation the coach, who also majored in Statistics, decides to identify all "outliers" in the data. Obviously, any player whose weight is above the regression line is not "under weight". So the only outliers the coach is interested in are those that are below the regression line. What is the lowest weight possible for a 69 inch player to not be considered "under weight"? Do not round. Submit Question MacBook Air O00 O00 F4 II F8 F2 F3 F5 F6 F7 F9 23 %24 & 8. E R T. Y F G K. C M. V B %#3

A football coach is looking for a way to identify players that are "under weight". The coach decides to get data for each player's height (x, in inches) and weight (y, in pounds), then does a linear regression. The results are: y = - 58 + 4x,r = 0.95 and the standard error is Se = 13. Since there is a strong linear correlation the coach, who also majored in Statistics, decides to identify all "outliers" in the data. Obviously, any player whose weight is above the regression line is not "under weight". So the only outliers the coach is interested in are those that are below the regression line. What is the lowest weight possible for a 67 inch player to not be considered "under weight"? Do not round. Submit Question MacBook Air >> F2 E3 000 E4 ES F6 F7 F8 F10 F9 24 4. %23 * 3. 8. 9. Y G H. J K C V M 3 BELK command