STAT151 Lecture Notes - Lecture 3: Total Variation, Statistical Process Control, Simple Linear Regression

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emeraldtortoise181

17 Apr 2015

School

University of Alberta

Department

Statistics

Course

STAT151

Professor

Rosana Fok

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STAT151 Full Course Notes

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Chapters 7 10: exploring relationship between variables - Definition: a scatter-plot is a graphical display for two quantitative variables. It uses the horizontal axis for the explanatory variable x and the vertical axis for the response y. The values of x and y for a subject are represented by a point relative to the two axes. The observations for the n subjects are n points on the scatter-plot. Example 1: find the scatter-plot of the following data x y. Definition: two quantitative variables are said to have a positive association when high value of x tend to occur with high value of y, and when low values of x tend to occur with low values of y. They are said to have a negative association when high values of one variable tend to pair with low values of the other variable, and low values of one pair with high values of the other.

Related Questions

Researchers measured the blood pressures of 22 students in

two situations: when the students were relaxed and when the students were taking an

important examination. The file

systolic.txt

lists the systolic and diastolic pressures for

each student in each situation. Dataset is available at

systolic_url = "https://mcs.utm.utoronto.ca/~nosedal/data/systolic.txt"

Use R

to answer each of the following questions. You have to show

all your work

to get

full credit.

Answers, even if correct, with no justifications will not receive any

marks

Using R

, compute the change in systolic pressure by subtracting systolic pressure when

relaxed from systolic pressure during the exam; call this variable

Using R

, repeat part a) for diastolic pressure. Call the resulting variable

Using R

, make a scatterplot of

versus

, fit a regression line to the data and add

this line to your plot. Use: 2 c) your last name as the main title for your plot. (In my

case it would be: 2 c) Nosedal).

Important note. Use

as your response variable and label horizontal and vertical axes.

d) What is the fitted regression model? Provide slope and y-intercept

, make a residual plot from the regression in part c). Does this plot call into

question the use of a linear model? Why?

Note. Use:

2 e) your last name

as the main title for your plot. (In my case it would

be:

2 e) Nosedal

f) Note the outlier in the residual plot (and on the scatterplot from part c)).

Using

, delete the outlier from the data set. Then repeat parts c) and e). Note. Use:

2 f )

your last name

as the main title for your plots. (In my case it would be:

2 f ) Nosedal

g) What is the fitted regression model (after the outlier has been removed)? Provide slope

Module 2 Minitab Assignment

Instructions:
Below you will find questions and a sample dataset. Please use the provided dataset to complete the tasks and to answer the questions.

As reported by the U.S. Census Bureau in Current Population Reports, the percentage of adults in each state and the District of Columbia who have completed high school is provided below.
Find the mean, median, and mode for this data set. Be aware that the mode does not always exist.
Find the range and standard deviation of this data set.
Write a sentence interpreting the mean and standard deviation.
Write a sentence interpreting the median.
Dataset:
State Percent - Dataset
Alabama 95
Alaska 89
Arizona 95
California 84
Delaware 80
Georgia 81
Illinois 88
Kansas 83
Louisiana 85
Massachusetts 85
New Mexico 91
New York 93
North Carolina 88
Oklahoma 85
Texas 88
Utah 91
Vermont 86
Washington 80
Wisconsin 81
Wyoming 95

(continued on next page)
Based on the following data,
Determine and interpret the first, second, and third quartiles.
Determine and interpret the interquartile range.
Construct a box-plot and describe the shape of the distribution.
Identify any outliers, if any.
Dataset:
96
59
55
111
76
91
60
57
84
123
56
89
61
72
89
72
81
88
75
79

(continued on next page)
This is a set of data from a sample of n = 11 items:
Produce a scatterplot of the data.
What does the plot suggest about the relationship between the variables?
Find and interpret the correlation coefficient.
Find and interpret the coefficient of determination.
Predict the value of y when x = 65. How much faith do you have in this prediction? Explain.
Dataset:
x y
46.1 150.8
47.6 150.2
45.5 141.3
43.1 167.4
44.5 166.7
36.9 121.7
47.4 143.6
44.8 186.1
41.3 166.2
33.5 140.4
34.4 132.9

sbmrgd

STAT151 Lecture Notes - Lecture 3: Total Variation, Statistical Process Control, Simple Linear Regression

STAT151 Full Course Notes

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