01:960:285 Lecture Notes - Lecture 29: Null Hypothesis, Statistical Hypothesis Testing, Dependent And Independent Variables

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maroonporcupine233

20 Oct 2016

School

Rutgers University

Department

Statistics and Biostatistic

Course

01:960:285

Professor

Shyam Moondra

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01:960:285 Full Course Notes

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The idea behind regression is that when there is significant linear correlation, you can use a line to estimate the value of the dependent variable for certain values of the independent variable. That is, when you reject the null hypothesis that rho=0 in a correlation hypothesis test. The value of the independent variable being used in the estimation is close to the original values. That is, you should not use a regression equation obtained using x"s between 10 and 20 to estimate y when x is 200. The regression equation should not be used with different populations. That is, if x is the height of a male, and y is the weight of a male, then you shouldn"t use the regression equation to estimate the weight of a female. The regression equation shouldn"t be used to forecast values not from that time frame. If data is from the 1960"s, it probably isn"t valid in the 1990"s.

Related Questions

The following data show Morning's Fair Value estimate and the Share Price for 28 companies. Fair Value is an estimate of a company's value per share that takes into account estimates of the company's growth, profitability, riskiness, and other factors over the next five years (Morningstar Stocks 500, 2008 edition).

Company	Fair Value ($)	Share Price ($)
Air Products and Chemicals	80	98.63
Allied Waste Materials	17	11.02
America Mobile	83	61.39
AT & T	35	41.56
Bank of America	70	41.26
Barclays	68	40.37
Citigroup	53	29.44
Costco Wholesale Corp	75	69.76
Covidien	58	44.29
Darden Restaurants	52	27.71
Dun & Bradstreet	87	88.63
Equifax	42	36.36
Gannett Co.	38	39.00
Genuine Parts	48	46.30
GlaxoSmithKline PLC	57	50.39
Iron Mountain	33	37.02
ITT Corporation	83	66.04
Johnson & Johnson	80	66.70
Las Vegas Sands	98	103.05
Macro vision	23	18.33
Marriot International	39	34.18
Nalco Holding Company	29	24.18
National Interstate	25	33.10
Portugal Telecom	15	13.02
Qualcomm	48	39.35
Royal Dutch Ltd.	87	84.20
SanDisk	60	33.17
Time Warner	42	27.60

(a) Develop the estimated regression equation that could be used to estimate the share price given the fair value.

(b) At the 0.05 level of significance, is there a significant relationship between the two variables.

(d) Do you believe the estimated regression equation would provide a good prediction of the share price? Use R2 to support your answer.

greenant419

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?

aquamarineporpoise659

Psychology of adulthood and aging;

Here is a question related to adulthood/aging that you think science canât answer:

Does age determine adulthood?

Then you will try to demonstrate how science could answer a related question. (Change the question to): When should a person be considered an adult?

Objectives:

Students should be able to speculate as to why two variables might be correlated, identify what a correlation between variables is not telling us, and anticipate what kind of research studies could further clarify a correlation between variables.

Students should be able to define operationalization, hypothesis, and be able to describe the scientific method by which psychologists study adulthood and aging.

a-First psychological variable

b-Give it a label

c-Briefly describe this variable.

Describe how this variable can be operationalized (that is, describe exactly how you determine which category or which value of the variable applies to a particular person or situation).

Second variable that you believe is related to your first variable.

a-Give it a label.

b-Briefly describe this variable.

c-Describe how this variable can be operationalized.

Once the variables are defined, the next step is to predict the relationship between these two variables by writing a hypothesis. A hypothesis is a prediction about the relationship between two or more variables. For now, assume that there is a causal relationship between the two variables even if it would be impossible or unethical to test a causal hypothesis. This means that changing a personâs score on one of the variables (the independent variable) would cause the personâs score on the other variable (the dependent variable) to change. For example, you might say, âIncreasing the amount of violent television that a person watches will cause that person to exhibit more aggressive behaviors.â

01:960:285 Lecture Notes - Lecture 29: Null Hypothesis, Statistical Hypothesis Testing, Dependent And Independent Variables

01:960:285 Full Course Notes

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