Suppose you fit the first-order multiple regression model y = beta_0 + beta_1 x_

Question

Suppose you fit the first-order multiple regression model y = beta_0 + beta_1 x_1 + beta_2 x_2 + epsilon to n = 25 data points and obtain the prediction equation y = -36.27 +1.8x_1 + 6.49x_2. The estimated standard deviations of the sampling distributions of beta_1 and beta_2 are 0.22 and 1.12, respectively. a. Test H_0: beta_2 = 0 against H_a: beta_2 notequalto 0. Use alpha = 0.05 b. Find a 99% confidence interval for beta_2. Interpret the interval a. The test statistic is (Round to three decimal places as needed) The p-value is (Round to three decimal places as needed.) the null hypothesis. There sufficient evidence to support the alternative hypothesis. b. What is the confidence interval? (Round to three decimal places as needed) Interpret this interval We are % confident that the true value of beta_2 lies in this interval (Type a whole number)

Explanation / Answer

a) TS = (b2^)/se(b2^)

= 6.49/1.12 = 5.794642

df = n-k-1= 25-2-1 = 22

p-value = 2 P(T >5.794642)

= 0.0000

since p-value < 0.05

we reject the null and there is sufficient evidence ....

b) 99 % confidence interval

t* for 99% confidence = 2.819

hence confidence interval is

(6.49 - 2.819 * 1.12 , 6.49 + 2.819 * 1.12)

=(3.33272 , 9.64728)

=(3.333,9.647)

we are 99 %   confident ...

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