Suppose you fit the? first-order multiple regression model yequalsbeta 0 plus beta 1 x 1 plus beta 2 x 2 plus epsilon to n equals 25 data points and obtain the prediction equation modifyingabove y with caretequals40.23 plus 1.33 x 1 plus 1.05 x 2. the estimated standard deviations of the sampling distributions of beta 1 and beta 2 are 0.20 and 0.20? , respectively. a. test upper h 0 : beta 2 equals 0 against upper h subscript a baseline : beta 2 not equals 0. use alphaequals0.05.
b. find a 99? % confidence interval for beta 2. interpret the interval. the test statistic is nothing. ? (round to three decimal places as? needed.) the? p-value is nothing. ? (round to three decimal places as? or do not) reject the null hypothesis. there (is or is not) sufficient evidence to support the alternative hypothesis.
c. what is the confidence? interval? (round to three decimal places as? needed.) interpret this interval. we are 99? %? confident that the true value of beta 2 lies in this interval.