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 β0 and β1 for this definition of x?

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(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)?

(c) How does the t test for nonzero β1 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?


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