STAT W21 Lecture Notes - Lecture 9: Interpolation, Dependent And Independent Variables, Linear Regression

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11 Sep 2017

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The sd line climbs (sinks, if r is negative) by sd(y) when you move to the right by sd(x) The sign of the slope of the sd line is the same as the sign of r and the size of the slope. In standard units, the slope of the sd line is one if r is greater than or equal to zero, and of the sd line is sd(y)/sd(x) equal to minus one if r is negative. Divides a scatterplot into class intervals of the horizontal (x) variable and plots the averages of the y values in those intervals against the midpoints of the intervals. Plots a typical value of y in each interval of values of x. The graph of averages lies systematically above the sd line when x is to the left of the point of averages and systematically below the sd line when x is to the right of the point of averages.

Related Questions

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

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

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?

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STAT W21 Lecture Notes - Lecture 9: Interpolation, Dependent And Independent Variables, Linear Regression

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