Quiz 2 Practice

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Western University *

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2037

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Statistics

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Jan 9, 2024

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SS1023/2037: Fall 2023 Quiz 2: Practice Problems QUESTION 1 The bone strengths of non-dominant and dominant arms were measured for 15 men. The fitted regression line for this data is: 𝑑??𝑖?𝑎?𝑡 = 2.74 + 0.936 × ??? − 𝑑??𝑖?𝑎?𝑡 Here are the data for four cases: Non-dominant Dominant 12.0 14.8 20.0 19.8 21.0 13.1 14.6 17.5 Calculate the residuals for these four cases. QUESTION 2 Consider the fitted regression line in Question 1. What is the predicted bone strength of a dominant arm, if the bone strength of the non-dominant arm is 17.3? QUESTION 3 For each of the following scenarios, make a scatterplot with 8 observations that show a moderate positive association, plus one that illustrates the unusual case. a) An outlier in x that is influential on the regression b) An outlier in x that is not influential on the regression c) An influential observation that is not an outlier in x QUESTION 4 This is a mosaic plot of the passengers aboard the Titanic , where red indicates people who died, and green those who survived. Write three conclusions you can make from this mosaic plot.

SS1023/2037: Fall 2023 QUESTION 5 A study shows that there is a positive correlation between the size of the hospital (measured by the number of bed) and the median number of days that patients remain in the hospital. Does this mean you can shorten your stay by going to a small hospital? What phenomenon is occurring here? QUESTION 6 A fellow researcher runs a linear regression for their data, and they tell you that their R-squared was 0.88, which means there is an 88% chance their model is correct. How do you explain what the R-squared actually is, and what it means in the case of their model? QUESTION 7 Simpson's Paradox occurs when a) We analyze two-way tables. b) A confounding variable rather than the explanatory variable is responsible for a change in the response variable. c) The direction of the relationship between two variables changes when the categories of a variable are taken into account. d) An association between two variables only exists due to chance. QUESTION 8 A researcher is examining the increasing number of wildfires in Minnesota, by counting the number of fires in the state from 1980 to 2020. They make a scatterplot with Year on the x-axis, the number of fires that year on the y-axis, and fit a simple linear regression. It is known that most of the fires in Minnesota are caused by people (as opposed to lightning), and the population of Minnesota has steadily increased over this time period. Other scientists have determined an upward trend in mean annual temperature in Minnesota, with an increase of 0.5 degrees Fahrenheit from 1975 to 2014. a) What is the response variable? What is the explanatory variable? b) What is a potentially confounding variable? QUESTION 9 Provide the equation of the fitted regression line and R squared for the following data: ? has standard deviation 1.1 and mean 3.2, and ? has standard deviation 12.4 and mean 104.3. The correlation between ? and ? is -0.67.

SS1023/2037: Fall 2023 QUESTION 10 Consider this two-way table, about the effects of running on joint pain: Experienced joint pain Yes No Runs over 30 miles per week Yes 380 785 No 82 215 a) What is the relative risk of running over 30 miles per week on joint pain? Interpret this value. b) What is the odds ratio from running over 30 miles per week? Interpret this value. The following 6 questions concern the following two-way table. For each of the 1317 passengers aboard the Titanic , we know their class (First, Second, Third) and their fate (survived, did not survive). The information can be summarized in a two-way table. QUESTION 11 Write the table with the joint distribution. QUESTION 12 What is the marginal distribution of Class? QUESTION 13 What is the conditional distribution of fate for passengers in second class? QUESTION 14 What is the conditional distribution of class for passengers who survived? QUESTION 15 What proportion of passengers in first class survived? QUESTION 16 What proportion of passengers who did not survive were in second class? Fate Class Survived Did not survive First 201 123 Second 118 166 Third 181 528

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