In Example 5.1, we compared relative decreases in stock market prices for the Consumer Staples and Financial categories of the S&P 500. Use a simple linear regression to model this data, where y is the relative increase, and x is a 0 if the stock is from the Consumer Staples category and a1 if from the Financial category.
(a) In words, how would you interpret ÃÂ²0 and ÃÂ²1 for this definition of x?
(b) Compare the results of the parameter estimates from your regression to the sample means within the groups. Are these consistent with your interpretations in (a)?
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(c) How does the t test for nonzero ÃÂ²1 from your regression compare to the pooled t test value? How does it compare to the unequal variance independent samples t test?
(d) What assumptions, if any, are violated by treating this data as a regression?