Suppose you fit the first-order multiple regression model = beta_0+ beta_1 + x_1

Question

Suppose you fit the first-order multiple regression model = beta_0+ beta_1 + x_1 + beta_2x_2 + epsilon to n = 25 data points and obtain the prediction equation y^- = 32.06 + 1.42x_1 + 2.86x_2. The estimated standard deviation of the sampling distributions of beta_1 and beta_2 are 0.27 and 0.44 respectively. a. Test H_0 beta_2 = 0 agilest H_a: beta_2 notequalto 0. Use alpha = 0.01. b. Find a 95% confidence interval for beta_2. Interpret the interval. a. The test satisfy is. (Round to three decimal places as needed.) The p-value is (Round to three decimal pleas as needed.) the null hypotheses. There sufficient evidence to support the alternative hypotheses. 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

Part a

Test statistic here is t value

Part b

T value = beta/std error = 1.42*sqrt(25)/0.47 = 15.10 corrosponding p value from table = 0.01

T value = beta/std error = 2.86 *sqrt(25)/0.44 = 32.5

corrosponding p value from table = 0.01

Part c

Confidence interval = beta +/- std error = 2.86 +/- 0.09

It implies the value of coefficient of beta lies netween 2.77 to 2.93

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