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ZOOM

STAT 326

LAB 3

due in lab

Lab 3 Stat 326

Unless otherwise specified, round all your final answers to the nearest cent.

Remember to include units with each answer when appropriate.

1. The act of reflection is a critical tool for learning. If we don't know what we have done correctly (or

incorrect), then we cannot learn from our mistakes and successes. Keeping this in mind, go back and

look at your lab 2 submissions. Discuss as a group all incorrect submissions. In the space provided

explain why your answers are wrong or incomplete. If your group didn't miss any points on lab 2,

write down two different parts your group struggled with (or almost missed) from lab 2. Describe

what specifically was difficult about these problems? The purpose here is to provide feedback for

yourself and group. Use this reflection to help you avoid making similar mistake and use this as a

reference for when you study for your exams.

2.

College Athletics:

In this example we are interested in trying to predict the expenses of a men's

college soccer team based on the expense of the men's golf team. A random sample of 200 colleges

and universities was taken of institutions with a men's golf team and a men's soccer team. In the

first problem we consider the following variables:

The Response Variable (

y

): Total Yearly Expense for the men's college/university soccer team (units

in thousands of dollars).

The Explanatory Variable (

x

): Total Yearly Expense for the men's college/university golf team (units

in thousands of dollars).

(a) Use JMP to create a scatter plot matrix (including correlation) between all variables. Based on

the scatter plot matrix describe the relationship between the expenses for the men's golf team

and the men's soccer team. (i.e. comment on the form, strength, direction of the relationship

and outlier) Are you concerned that this outlier mentioned above may influence the calculation

of the least squares regression line? Explain.

Stat 326: Lab 3:

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(b) True or False

(Circle one.)

: If we identify an outlier, regardless of the example, we should

automatically delete this observation and work with a reduced data set.

(c) Write down the theoretical (population) model that would be appropriate to describe the linear

relationship between the two variables on which this study focuses. Be sure to use the correct

notation.

Regardless of your previous answers, the rest of this example will use the model

based on all 200 observations.

(d) Using the full dataset, use JMP to find the estimated least squares regression line. Be sure this

estimated equation is based on the full dataset (200 observations). Write the estimated model

in the space provided below. It is important to use correct symbols here. Specifically define

y

and

x

in this example.

x

:

y

:

Estimated Least squares regression line:

(e) Provide an interpretation for the estimated slope within the context of the data.

(f) In simple linear regression the residual plot is used to check which assumption(s)? Clearly list

all relevant assumptions in the space below.

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Stat 326: Lab 3:

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(g) What variables should be on each axis of the residual plot described above? Use the variable

names based on the context of this example. (There is more than one correct answer.)

x-axis:

y-axis:

(h) Create the residual plot and comment on all appropriate assumptions.

(i) The normality assumption is checked using which plot? The normal quantile plot of the

.

(j) Create the normal quantile plot and comment on the appropriate assumptions.

Regardless of any concerns with the assumptions continue to answer the following

questions.

(k)

percent of the variation in the

is explained by the simple

linear

regression model between

(l) Assume that Iowa State University is considering adding a male soccer team. In a recent year

the Iowa State golf team had yearly expenses of $849,000. Use this simple linear regression

model to predict the yearly expenses for a male soccer team at Iowa State University?

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Stat 326: Lab 3:

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(m) Use your simple linear regression model to calculate the residual for a school with male golf

team expenses of

and male soccer team expenses of

?

The value in the blanks will show up in your Canvas Quiz. Each student will have a a different

pair of numbers. Record your answer assuming the units for the residual are $1000. If the

answer if $7,632 type 7.632 as your submission. Use at least 3 decimal places for all parts of

your calculation.

(n) Create a 98% confidence interval for the slope associated with male golf team expenses. Report

the lower and upper bounds

(o) Based on the information from part 2n, is there evidence to discredit a claim that institutions

with $20,000 more in male golf team expenses will on average have $50,000 more in additional

male soccer team expenses. Clearly explain your answer.

(p) Is there evidence that colleges/universities with higher men's Golf expenses are generally related

to higher Men's soccer expenses? Answer this question using an appropriate hypothesis test.

(q) Don't forget to upload your output to Canvas.