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Textbook Guide Statistical Sciences: Scatter Plot, Mathematical Diagram, Dependent And Independent Variables

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grayraven524
1 Dec 2016
School
UTSG
Department
Statistical Sciences
Course
STA130H1
Professor
all

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STA130H1 Full Course Notes
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The control (aka independent or explanatory) variable is plotted along the horizontal axis, while the measured (aka dependent or response) variable is plotted along the vertical axis (figure 1). Plotting the data in this way allows us to illustrate the degree of correlation between two variables. There are many different types of correlation (figure 2). Variables that have a positive association are high values of one variable occurring with high values of the other variable or low values of one variable occurring with low values of the other variable (e. g, figure 2a). Variables that have a negative association are high values of one variable occurring with low values of the other variable (e. g. , figure 2b). These two examples feature linear graphs because we can see the resemblance of a line forming from the plotted data. Some data show correlation in a non- linear fashion (e. g. , figures 2c and 2d), while others how no correlation at all (e. g. , figure 2e).

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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.

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?