R
#if you've already installed the package you do not need to run this line again install.packages ("alr4") #load the package (must load the package every time you start a new session of R) library (alr4) data (oldfaith) (a) What are the explanatory and response variables in this problem? (b) Use the lm () function to fit a model. Provide the summary output of the fitted model. (c Check the assumptions of this model. Make sure to show any plots you created to check these assumptions (d) Based on the results of your fitted model, summarize the results in a way that would be useful to a Park department official who is not familiar with statistics. Hint: interpret the intercept and slope estimate in the contert of the model (e) Using the fitted model output (or a function of the output values), identify or solve for (i) S (also written as ) (ii) SXX hint: use SE(Bi) (iii) SXY hint: use SXX and 1 (f) Complete a hypothesis test that tests for a one to one relationship with duration and interval. In other words for every second longer Old Faithful erupts does that increase the interval time by one minute? (i) Write out the null and alternative hypotheses (ii) Calculate the test statistic, what distribution does the test statistic have under Ho? (iii) Calculate the p-value (hint: use the pt) function) (iv) Make a conclusion at a 5% significance level (g) Fill in the blank and construct the correct interval type: Tourists who hiked up to Old Faithful saw an o interval for the expected time a tourist will have to eruption last 250 seconds, give a 90% wait for the next eruption. (h) Fill in the blank and construct the correct interval type: Bob is tourist and just hiked up to Old Faithful interval for the predicted time Bob will and saw an eruption last 250 seconds. Give a 90% have to wait for the next eruption o .. (i) In the above two interval problems, is one interval wider than the other? If so why? #if you've already installed the package you do not need to run this line again install.packages ("alr4") #load the package (must load the package every time you start a new session of R) library (alr4) data (oldfaith) (a) What are the explanatory and response variables in this problem? (b) Use the lm () function to fit a model. Provide the summary output of the fitted model. (c Check the assumptions of this model. Make sure to show any plots you created to check these assumptions (d) Based on the results of your fitted model, summarize the results in a way that would be useful to a Park department official who is not familiar with statistics. Hint: interpret the intercept and slope estimate in the contert of the model (e) Using the fitted model output (or a function of the output values), identify or solve for (i) S (also written as ) (ii) SXX hint: use SE(Bi) (iii) SXY hint: use SXX and 1 (f) Complete a hypothesis test that tests for a one to one relationship with duration and interval. In other words for every second longer Old Faithful erupts does that increase the interval time by one minute? (i) Write out the null and alternative hypotheses (ii) Calculate the test statistic, what distribution does the test statistic have under Ho? (iii) Calculate the p-value (hint: use the pt) function) (iv) Make a conclusion at a 5% significance level (g) Fill in the blank and construct the correct interval type: Tourists who hiked up to Old Faithful saw an o interval for the expected time a tourist will have to eruption last 250 seconds, give a 90% wait for the next eruption. (h) Fill in the blank and construct the correct interval type: Bob is tourist and just hiked up to Old Faithful interval for the predicted time Bob will and saw an eruption last 250 seconds. Give a 90% have to wait for the next eruption o .. (i) In the above two interval problems, is one interval wider than the other? If so why
