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STAT 100 Chapter Notes - Chapter 15: Dependent And Independent Variables

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coralmole465
14 Oct 2014
School
Simon Fraser University
Department
Statistics
Course
STAT 100
Professor
Derek Bingham

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STAT 100 Full Course Notes
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STAT 100 Full Course Notes
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Document Summary

A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x. Regression is the name for statistical methods that fit some model to data in order to predict a response variable from one or more explanatory variables. The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible. y=a+bx. Prediction outside the range of available data is referred to as extrapolation. The square of the correlation, r2, is the proportion of the variation in the values of y that is explained by the least-squares regression of y on x. A strong relationship between two variables does not always mean that changes in one variable cause changes in the other.

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Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

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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
.
a)
Using R
, compute the change in systolic pressure by subtracting systolic pressure when
relaxed from systolic pressure during the exam; call this variable
X
.
b)
Using R
, repeat part a) for diastolic pressure. Call the resulting variable
Y
.
c)
Using R
, make a scatterplot of
Y
versus
X
, 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
Y
as your response variable and label horizontal and vertical axes.
d) What is the fitted regression model? Provide slope and y-intercept
explicitly
.
Use R
to find them.
e)
Using R
, 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
R
, 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
and y-intercept
explicitly
.
Use R
to find them.

Opeele Kyinkafa sells different used 2005 GM cars in excellent condition. The value or the retail price (Price) of a car is dependent on a variety of characteristics such as number of miles the car has been driven (Mileage), manufacturer of the car (Make) such as Buick, Cadillac, Chevrolet, Pontiac, SAAB, and Saturn. The car price is also influenced by the body type (Type) such as sedan, convertible, coupe, hatchback and wagon. It is also affected by number of cylinders (Cylinders) in the engine, the engine size (Liter), cruise control which is an indicator variable representing whether the car has cruise control (yes) or no otherwise and Sound indicator representing whether the car has upgraded speakers (yes) or no otherwise. All cars in this data set were less than one year old when priced and considered to be in excellent condition. Determine which major variables are dummies and are dynamic? Identify 3 potential unobserved heterogenous factors in this dataset. Display the full descriptive statistics of the data in R. Why do you think some variables are starred (*)? What is the median for “price”, standard deviation for “mileage”, skewness for “cylinder” and mean for “sound”? Test if “price” is normally distributed using histogram, kernel density plot and the shapiro wilk test. Create a red scatterplot matrix of price, mileage, cylinder, liter, make. From your graph, is the correlation between price & mileage positive or negative? What’s the pearson correlation coefficient between price & mileage and between “cylinder” & “liter” correct to 2 d.p Create a correlation matrix of the dataset by finding the apt R command for converting all string/dummy variables From the matrix, identify 2 potentially good predictors? Identify 3 pairs of variables that are mostly multicollinear. Which 2 pairs of variables are least correlated? Identify 3 pairs of variables most highly correlated with Cylinder Generate a simple regression plot of price on mileage with a re fitted line. Run the whole multiple regression model (label the equation as "regprice") & use it to answer the other questions. Specify the regression model for the whole data keeping the exact names of the variables. Write the estimated regression equation. In one sentence, which variables are significant and which are not? Justify Is the regression model justifiable? Explain Interpret the coefficient of Mileage, MakeCadillac, TypeSedan, Cylinder, & Cruiseyes. Compare the price of a car with 130,000 mileage, 6 cylinders, 3.8 liters, with cruise and sound, was manufactured by Pontiac with a convertible body type with that of the price of a car with four cylinders, 120,000 mileage, 3.8 liters, without cruise nor sound, was manufactured by Cadillac with a hatchback body type. Which factor(s) appears to be causing a comparative difference (if any)? Using only the VIF, which one of the pairs of variables selected to be multicollinear may be deleted? Justify?