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By: F. Pranck, M.B. B.A.O., M.B.B.Ch., Ph.D.

Medical Instructor, William Carey University College of Osteopathic Medicine The interval is of the form: ^ ± z/2 ^^ for large samples allergy testing labcorp purchase loratadine 10 mg without prescription, or ^ ± t/2 ^^ for small samples where the random error terms are approximately normal allergy symptoms headache fatigue purchase 10 mg loratadine free shipping. Also allergy treatment 3 year old discount loratadine 10mg without prescription, xx we have n - 2 degrees of freedom instead of n - 1 allergy report nyc purchase loratadine, since the estimate s2 has 2 estimated paramters used in it (refer back to how we calculate it above). Note that if 1 > 0, then multiple dose gemfibrozil clearance is higher among patients with high creatinine clearance (lower in patients with impaired renal function). Conversely, if 1 < 0, the reverse is true, and patients with impaired renal function tend to have higher clearances. Finally if 1 = 0, there is no evidence of any association between creatinine clearance and multiple dose creatinine clearance. Since the authors were concerned that the clearance would be lower in these patients, they stated that dosing schedules does not need to be altered for patients with renal insufficiency. Hypothesis Tests Concerning 1 Similar to the idea of the confidence interval, we can set up a test of hypothesis concerning 1. Also, since our test statistic is negative, and we conclude that 1 < 0, just as we did based on the confidence interval in Example 7. One measure of this association that is often reported in research journals from many fields is the Pearson product moment coefficient of correlation. A value of r close to 0 implies that there is very little association between the two variables (y tends to neither increase or decrease as x increases). A positive value of r means there is a positive association between y and x (y tends to increase as x increases). Similarly, a negative value means there is a negative association (y tends to decrease as x increases). Also a test that the population correlation coefficient is 0 (no linear association between y and x) can be conducted, and is algebraically equivalent to the test H0: 1 = 0. Another measure of association that has a clearer physical interpretation than r is r2, the coefficient of determination. There is a moderate, negative correlation between multiple dose gemfibrozil clearance and creatinine clearance. Further, r2 can be interpreted as the proportion of variation in multiple dose gemfibrozil clearance that is "explained" by the regression on creatinine clearance. We would like to break these deviations into two parts, the deviation of the observed value from its fitted value, ^ ^ yi = 0 + 1 xi, and the deviation of the fitted value from the overall mean. This is similar in nature ^ to the way we partitioned the total variation in the completely randomized design. We will also find this decomposition useful in subsequent sections when we have more than one predictor variable. While the amount of math can become overwhelming and involves matrix algebra, many computer packages exist that will provide the analysis for you. In this section, we will analyze the data by interpreting the results of a computer program. It should be noted that simple regression is a special case of multiple regression, so most concepts we have already seen apply here. In general, if we have p explanatory variables, we can write our response variable as: Y = 0 + 1 x1 + + p xp +. Again, we are writing the random measurement Y in terms of its deterministic relationship to a set of p explanatory variables and a random error term. We make the same assumptions as before in terms of, specifically that it is normally distributed with mean 0 and variance 2. The parameters i represent the change in the mean response when the ith explanatory variable changes by 1 unit and all other explanatory variables are held constant. The Analysis of Variance table will be very similar to what we used previously, with the only adjustments being in the degrees of freedom. Note that if H0 is true, then the mean response does not depend on the levels of the explanatory variables. We interpret this to mean that there is no association between the response variable and the set of explanatory variables. Note that if we fail to reject the null hypothesis that i is zero, we can drop the predictor xi from our model, thus simplifying the model. Note that this test is testing whether xi is useful given that we are already fitting a model containing the remaining p - 1 explanatory variables.   