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The last lessons have spent a lot of time describing the slope and intercept terms (and their variances) of the one-variable sample regression function. We also know that for any particular value of the independent variable (call it X0), that the predicted value of Y0 is Y0 = B0 + B1X0 . (This is sometimes called a "point prediction.")
a) Prove that Y0 is an unbiased estimator of E[Y0|X0].
b) Derive the formula for the variance of Yo . Show at least two steps in this derivation.
X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities.
Report a table of marginal means for each level of each of the three factors.
A research firm reported that 15% of those surveyed stated their health as poor, 26% as good, 40% as very good, and 19% as excellent. A health professional in Chicago wanted to determine if people in Chicago had similar feelings toward their healt..
Use the marginal probabilities of school quality, school cost or convenience, and other to comment on the most important reason for choosing a school.
You manufacture and sell an iron rod whose electrical conductivity is supposed to be 10.1. You plan to make 6 measurements of the conductivity of a rod you plan to sell.
A test of hypothesis is conducted at the .05 level of significance to test either or not the population correlation is zero.
A concessionaire for the local ballpark has made a table of conditional values for the different alternatives also states of nature
For the samples summarized below, test the hypothesis at ∞ =.05 that the two variances are equal. Variance Number of data values Sample 1 19 8 Sample 2 9 18
Test the equality of the means of three populations.
The following data shows the packages gathered for delivery for ten days and the proportion of packages received not delivered to the customers at expected time.
Determine probability that number of boats constructed next month will be between 4 and 7 (both inclusive).
The pooled variance of two samples is:
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