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Q1. Suppose that X = (xij)nx2 is an observed data matrix from a bivariate normal distribution N(μ,σ2I), where I is the 2 x 2 identity matrix. Find the maximum likelihood estimates of μ and σ2.
Q2. In this problem we will perform regression analysis on the sepal and petal measurements of the first 50 flowers in the Iris data. We want to use the sepal length and width and the petal length of a flower to predict its petal width. That is, the response variable is Y = iris[1:50,4] and the explanatory variables are X = (Xi | X2 | X3) = iris[1:50,1:3]. Assume a linear regression model that Y = β0 + Σ3 j=1 βjXj + ε, where ε is the error (residual) vector.
(a) Find the least square estimate of β = (β0.........β3) and the sum of squared residuals.
(b) If we want to use two of the three explanatory variables to predict Y, which two should we choose? Justify your answer.
Find the confidence interval of the true proportion of students to receive a 3.0 GPA. Find the Z score, standard error, range, and your conclusion in a sentence.
By using the age midpoints x and the percentages of nurses, do we have a valid probability distribution? Describe.
If we wish to be 95% certain of avoiding a Type I error, use these data to examine differences in the average distance traveled to the two clinics.
Make an interval estimate the population means score for the daycare children so that you are 95% confident that the true mean is in your interval.
Give an example of a single polynomial with degree 3, whose value is 4 when the variable is equal to 1. Give an example of a single polynomial with degree 3, whose value is 29 when the variable is equal to 2.
From the fourth quarter of 1997 to the first quarter of 1998, revenues declined. What happened on a seasonally adjusted basis? d)Compute the forecast for the second quarter of 2002. e)Find the regression equation to predict the long term trend in th..
If the class does well on an exam, then the next exam is equally likely to be any of the three types. If the class does badly, then the next exam is always type 1. What proportion of exams are type 1, 2, and 3?
Five homes are selected at random: What is the probability none of the six selected homes have a security system? (Round your answer to 3 decimal places.)
The sales of the bicycle (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded. State the multiple regression equation.
Find the midrange for the following group of data items: what is the midrange rounded to the nearest tenth?
If 1 adult male is randomly selected and is assumed to have 20 pounds of carry-on baggage, find the probability that his total is greater than 195 pounds. Round your answer to three decimal places.
The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude? Determine the p-value and perform the test.
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