Homework 3 solution PDF

Preview

Summary

Homework 3 solution...

Description

STAT 420: Homework 3 Summer 2016, Dalpiaz and Unger Due: Friday, July 1 by 11:50 PM CDT Solution Exercise 1 (Using lm for Inference) Exercise 2 (Using lm for Inference) Exercise 3 (Inference “Without” lm ) Exercise 4 (Simulating Sampling Distributions) Exercise 5 (Simulating Confidence Intervals)

Solution Exercise 1 (Using lm for Inference) For this exercise we will again use the faithful dataset. Remember, this is a defau R , so there is no need to load it. You should use ?faithful to refresh your memor background of this dataset about the duration and waiting times of eruptions of the geyser (http://www.yellowstonepark.com/about-old-faithful/) in Yellowstone Natio (https://en.wikipedia.org/wiki/Yellowstone_National_Park). (a) Fit the following simple linear regression model in R . Use the eruption duratio response and waiting time as the predictor.

Yi = β0 + β1 xi + ϵi Store the results in a variable called faithful_model . Use a t test to test the signifi regression. Report the following: The null and alternative hypotheses. The value of the test statistic. The p-value of the test. A statistical decision at α = 0.01 . A conclusion in the context of the problem

faithful_model = lm(eruptions ~ waiting, data = faithful) summary(faithful_model)

## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##

Call: lm(formula = eruptions ~ waiting, data = faithful) Residuals: Min 1Q -1.2992 -0.3769

Median 0.0351

3Q 0.3491

Max 1.1933

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1.87402 0.16014 -11.7...