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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.
Suppose that the population of heights of male college students is approximately normally distributed with mean m of 69.09 inches and standard deviation s of 4.71 inches.
How much variability will you have if you predict sales with this model?
A survey conducted by the American Automobile Association showed that the family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls results in a sample mean of $252...
The average age of the women was 36.97 with a standard deviation of 8.893. If a 95% confidence interval is calculated to estimate the difference between the two average ages, what is the margin of error? Assume both population standard deviations ..
Plot fitted values against residuals. Does this plot point out any problems with homoscedasticity?
A psychologist is investigating the hypothesis that children who grow up as the only child in the household develop different personality characteristics than those who grow up in larger families.
What is the 95% confidence interval estimate of the population mean cost for a prescription of Zocor?
What is the probability that he will answer all questions correctly?
Suppose the random variable x is best described by a normal distribution with µ = 24 and σ = 2.7. Find the z-score that corresponds to each of the following x values.
At.01 significance level, is there difference in mean number of times men and women order take-out dinners in month? Determine the p -value?
Determine the probability of choosing the area code at random which ends in the odd number if first digit cannot be 1 or 0?
For each of the F statistics given above find the degrees of freedom and an approximate P-value. Summarize the results of these tests.
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