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UC Irvine, Statistics 110/201
Homework Assignment #1
Assigned October 1, 2018
Due October 10, 2018
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Question 1
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“If you have borderline high blood pressure, taking magnesium supplements may help, Japanese re-
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searchers report. Blood pressure fell significantly in subjects who got 400-500 milligrams of magnesium
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a day for four weeks, but not in those getting a placebo” (USA Weekend, 22-24 May 1998, p. 11)
(a) Do you think this a randomized experiment or observational study. Explain your answer
(b) What are the explanatory and response variables in this study?
(c) Do you think the relationship found in this study is a causal one, in which taking magnesiumactually causes blood pressure to be lowered? Explain.
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Question 2
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A [hypothetical] study measured several variables for a random sample of children entering first grade.
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One of the variables was the amount of time parents or care-givers spent reading to the child during the
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first four years of life. Another variable was the child’s score on a placement test consisting of solving
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word and arithmetic puzzles. A positive relationship was found between these two variables.
(a) Was the study more likely to have been an observational study or a randomized experiment? Explainhow you know.
(b) What is the explanatory variable and what is the response variable in the reported relationship?(c) After the study, one of the investigators was quoted saying, “Parents, if you want your children toscore higher on our placement test, you need to read to them more when they are very young.” Doyou agree with the investigator’s quote? Explain why or why not.
(d) Identify a possible confounding variable. Explain how the variable you identified is a confoundingvariable.
(e) Identify a possible precision variable. Explain how the variable you identified is a precision variable.- Question 3
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Answer question 0.2 in the textbook on pages 13-14 of the textbook. For the students who have not
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purchased the textbook yet here is the question: Refer to the data described in Exercise 0.1 that a
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statistic professor records for her students. For the following questions, identify the response variable
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and the explanatory variable(s). Also, classify each variable as quantitative or categorical. For categorical
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variables, also indicate whether the variable is binary.
(a) Do the proportions of left-handers differ between males and females on campus.
(b) Are sleeping time, exam 1 score, and number of quizzes taken useful for predicting time spent onthe final exam?
(c) Does knowing a student’s gender help predict his or her major?
(d) Does knowing a student’s political inclination and time spent sleeping help to predict his or hergender?
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Question 4
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Complete the following algebra problems:
(a) Find the equation for the linear function which connects the two points (−1, 3) and (2,−1).(b) Find the equation for the linear function which connects the following three points (4, 0, 1), (2, 5, 0)and (0, 3, 2). Note that the resulting equation is a plane in R3 in the form of z = ax + by + c, thusyou need to find the values of a, b, c such that the plane goes through the three points.
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For questions 5-9 use the Sparrows dataset to answer the questions. In this set of questions we are going to
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investigate the health of Savannah sparrows. To measure the health of the sparrows, investigators proposed
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using the weight (in grams) of a sparrow as an analogue to the overall health of the sparrow. However, weight
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is a function of the physical size of the bird. The investigators chose to use wing length (in millimeters) to
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measure the physical size of the bird. A stratified sample of 116 sparrows were collected in Kent Island, New
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Brunswick, Canada.
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Question 5
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Identify the explanatory variable and response variable.
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Question 6
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Both variables, wing length and weight, are quantitative variables. Create a scatterplot of the data. Put
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the explanatory variable on the x-axis and the response variable on the y-axis (be sure to label both
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axes). Based on the scatterplot you created, do you believe that a linear regression equation is justified
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to examine the relationship between these two variables?
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Question 7
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The Sparrows dataset is available on the course website. Read the dataset in to R and create a linear
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regression model. Use the model you created to answer the following questions.
(a) Print the summary output of the model you created in R.
(b) Give the value of the intercept, and explain what it would represent in the context of this situation.Does it have a meaningful interpretation? Explain.
(c) Give the value of the slope, and interpret what it means in the context of this situation.
(d) One particular sparrow had a wing length of 29 mm and weighed 17 grams. Find the residual forthis particular sparrow.
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Question 8
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An additional variable called “Treatment” is in the data set, representing the type of nest the sparrow
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was sampled from. One of the “treatments” is a “Control” nest. Rerun the regression in R using only
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the sparrows from the “Control” group, then answer the following questions.
(a) Print the summary of the output of the model you created in R.
(b) Compare the regression equation from question 7a and 8a. Are the intercepts similar? Are theslopes similar?
(c) Compute the residual for the sparrow with a wing length of 29 mm and a weight of 17 grams. Isthe residual in question 7d smaller than the one you just calculated? Which regression equationgave a better predicted weight for the particular sparrow.
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Question 9
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Clearly, the study is an observational study as the investigators cannot assign a sparrow a physical
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condition. However, if the investigators concluded that the two variables are related, do you believe
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their conclusion would be valid for all Savannah sparrows?
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