2. A study is conducted in patients with HIV. The primary outcome is CD4 cell count which is a measure of the stage of the disease. Lower CD4 counts are associated with more advanced disease. The investigators are interested in the association between vitamin and mineral supplements and CD4 count. A multiple regression analysis is performed relating CD4 count to use of supplements (coded as 1=yes, 0=no) and to duration of HIV, in years (i.e., the number of years between the diagnosis of HIV and the study date). For the analysis, Y=CD4 count.Y = 501.41 + 12.67 Supplements – 30.23 Duration of HIVA. What is the expected CD4 count for a patient taking supplements who has had HIV for 2.5 years?Y = 438.505B. What is the expected CD4 count for a patient not taking supplements who was diagnosed with HIV at study enrollment?Y = 471.18C. What is the expected CD4 count for a patient not taking supplements who has had HIV for 2.5 years.= 425.835I would like to know if calculated correctly. Thank you for your help.

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?

If there is no significant correlation between the response and explanatory variables, would the slope of the regression line be (a) positive (b) negative (c) zero?

In a simple linear regression model with one predictor variable, what is the coefficient of determination (R-squared) if the Pearson's correlation coefficient between the predictor and response variable is 0.6?