STAT151 Lecture : Linear Regression and Correlation Done in LaTeX

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silverseal471

22 Dec 2011

School

University of Alberta

Department

Statistics

Course

STAT151

Professor

Alireza Simchi

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STAT151 Full Course Notes

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Document Summary

Response or dependent variable: the outcome variable on which comparisons are made. Explanatory or independent variable: de nes the group to be compared with respect to the values of the response variable. Scatter-plot: 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 subjects are points on the scatter-plot. Positive association: when two quantitative variables to have a high values of x with high values of y , and low values of x with low values of y . Negative association: two quantitative variables with a high value of x tending to occur with low value of y , and vice versa. 1001234567891002468x axisy axis1001234567891002468x axisy axisnote: when the correlation is non-linear, it is best to nd an intermediary.

Related Questions

Consider a regression study involing a dependent variable y, and quantitative independent variable , and a categorical independent variable with three possible levels (level 1, level 2, and level 3).

a. How many dummy variables are required to represent the categorical variable?

b. Write a multiple regression equation relating and the categorical variable to y.

plumgoose301

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

Identify the true statements about the correlation coefficient, r.

a.) The correlation coefficient is not affected by outliers.

b.)The value of r ranges from negative one to positive one.

c.) When the data points in a scatter plot fall closely around a straight line that is either increasing or decreasing, the correlation between the two variables is strong.

d.) A correlation coefficient of zero means that no relationship exists between the two variables.

e.) If two variables are positively correlated, when one variable increases, the other variable decreases.

f.) The sign of r describes the direction of the association between two variables.

bluefly693

STAT151 Lecture : Linear Regression and Correlation Done in LaTeX

STAT151 Full Course Notes

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