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Model 1: Let's consider the logistic regression model, which we will refer to as Model 1, given bylog(pi / [1-pi]) = 0.25 + 0.32*X1 + 0.70*X2 + 0.50*X3 (M1),where X3 is an indicator variable with X3=0 if the observation is from Group A and X3=1 if the observation is from Group B. The likelihood value for this fitted model on 100 observations is 0.0850.(4) For X1=2 and X2=1 compute the log-odds for each group, i.e. X3=0 and X3=1.(5) For X1=2 and X2=1 compute the odds for each group, i.e. X3=0 and X3=1. (6) For X1=2 and X2=1 compute the probability of an event for each group, i.e. X3=0 and X3=1. (7)Using the equation for M1, compute the relative odds associated with X3, i.e. the relative odds of Group B compared to Group A. (8) Use the odds for each group to compute the relative odds of Group B to Group A. How does this number compare to the result in Question #7. Does this make sense?Model 2: Now let's consider an alternate logistic regression model, which we will refer to as Model 2, given bylog(pi / [1-pi]) = 0.25 + 0.32*X1 + 0.70*X2 + 0.50*X3 + 0.1*X4 (M2),where X3 is an indicator variable with X3=0 if the observation is from Group A and X3=1 if the observation is from Group B. The likelihood value from fitting this model to the same 100 observations as M1 is 0.0910.(9) Use the G statistic to perform a likelihood ratio test of nested models for M1 and M2. State the hypothesis that is being tested, compute the test statistic, and test the statistical significance using a critical value for alpha=0.05 from Table A.3 on page 375 in Regression Analysis By Example. From these results should we prefer M1 or M2?
The following data represents the pulse rates of ten randomly selected females after stepping up and down on a 6-inch platform for 3 minutes. Pulse is measured in beats per minute. Compute the sample mean pulse.
In this problem set you will get some practice performing hypothesis tests for two samples. If you use Statdisk to perform any portion of these analyses, please include the results, label them, and refer to them accordingly in your interpretations..
A company has 25 cars of this model. What is the probability that the mean nitrogen oxide emissions of these cars is above the 0.3g/mi limit?
Assuming these data are from two independent groups, calculate dfX, dfY, and dftotal for the data above. Determine the critical values for t based on the df you calculated for the question above, assuming a two-tailed test with a p level of 0.05.
Simple random sample from the students in the university. Find the probability that the average number of study hours for this group is between 21 and 23 hours.
If 20 students in the class said they frequently experience stress in their daily lives, would you be surprised? Explain and use statistics to support your answer
What is the probability that a simple random sample of automobile insurance polocies will have a sample mean within 25.
Why are you no longer directly comparing sample means? How does using the F test - the analysis of variance (ANOVA) reduce your Type I error rate? What is the difference between a within-groups and a between-groups variance?
Use the Excel COUNTIF function to determine the number of tires that last longer than 40,000 miles. What is your estimate of the percentage of tires that will exceed 40,000 miles?
In case of fire, the probability that D1 operates correctly is 0.95 and the probabilty that D2 operates correctly is 0.92. Find the probability that the sprinkler system will come on.
can we conclude that the mean assembly time for this component exceeds 3 minutes? What error could be made in this case? Describe it in words.
Construct the 90 percent confidence interval for the proportion of checking account customers who have a Visa card with the bank. (Round your answers to 3 decimal places.)
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