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PR 680 Lecture Notes - Lecture 60: Scatter Plot

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School
Ball State University
Department
Public Relations
Course
PR 680
Professor
Dr. Sungwon Chung

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Document Summary

The correlation coefficient is a popular way of summarizing a scatterplot into one single number between -1 and 1. As an example, say you have a scatterplot that shows four movies. On the x axis, the movies length is shown and on the y axis, the rating for the movie between 0 and 5 stars. If in the example, your slope is positive, which means the correlation coefficient will be positive as well. So if the slope is positive, that means the correlation coefficient will have to be between 0 and. Then in the second case in another data set, the slope is negative because the longer the movies tend to get the worse ratings. So the slope, being negative, means the correlation coefficient will be negative as well between. Then there"s a third case showing that the slope is perfectly straight. In this data set, there is no real difference between long and short movies and their rating.

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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.

ECON 3050

Q24. The coefficient of determination (r2) is calculated as 0.49, then the correlation coefficient:

Cannot be determined without the data

Should be - 0.70 or 0.70

Should be 0.

Neither of the above

Q25. A regression line is used for all of the following except one. Which one is not a valid use of a regression line?

To estimate the average value of Y at a specified value of X.

To predict the value of Y for an individual, given that individual's X-value.

To estimate the change in Y for a one-unit change in X.

To determine if a change in X causes a change in Y.

Q26. Which choice is not an appropriate description of Yˆ in a regression equation?

Estimated response

Predicted response

Estimated average response

Observed response

Q27. Which of the following is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables?

Compute a regression line from a sample and see if the sample slope is 0.

Compute the correlation coefficient and see if it is greater than 0.5 or less than −0.5.

Conduct a test of the null hypothesis that the population slope is 0.

Conduct a test of the null hypothesis that the population intercept is 0.

Q28. There is no relationship between variables unless the data points lie in a straight line.

True

False

Q29. The sample regression analysis

Is the same as the population regression line

Is used to estimate the population regression line

Shows the true relation between dependent and independent variables

None of the above.

Q30. In regression, a dependent variable is sometimes called a predictor variable.

True

False

Q31. In a linear regression equation of the form y = a + bx, the intercept shows

The amount that y changes when x changes by one unit

The amount that x changes when y changes by one unit

The value of y when x is zero

The value of x when y is zero.

Q32. In a linear regression equation of y = a + bx, the slope b shows

Y / b

X / b

Y / X

X / Y

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?