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# Pearson Product-Moment Correlation

The Pearson product-moment correlation coefficient is a measure of a linear correlation between two variables X and Y, giving a value between +1 and -1 inclusive. It is widely used in the science as a measure of the strength of linear dependence between two variables. Pearson’s correlation coefficient between two variables is defined as the covariance of the two variables divided by the product of their standard deviation. The form involves a product moment that is the mean of the product of the mean-adjusted random variables; hence the modifier product moment in the name.

The absolute value of both the sample and population Pearson correlation coefficients are less than or equal to 1. Correlations equal to 1 or -1 correspond to data points lying exactly on a line, or to a bivariate distribution entirely supported on a line. A key mathematical property of the Pearson correlation coefficient is that it is invariant to separate changes in location and scale in the two variables.

The correlation coefficient ranges from -1 to 1. A value of 1 implies that a linear equation describes the relationship between X and Y perfectly with all data points lying on a line for which Y increases as X increases.  A value of -1 implies that all data points lie on a line for which Y decreases as X increases. A value of 0 implies that there is o linear correlation between the variables.

### Determining correlation between two variables based on r-values

Review the SPSS output file which reports the results of the correlation to see if there is a correlation between the cost of beer and the number of calories it contains or the cost of beer and the volume of alcohol it contains. Answer the following questions based on your observations of the SPSS output file: Based on the co

### Significance of correlation coefficient - test statistic

A pharmaceutical company conducts a study to evaluate the relationship between length of time taking drug X and size of tumor. They enlist 2400 patients with the same type of benign tumor who have been on drug X for varying lengths of time (measured in days). They find that the longer the patient is on the drug, the smaller the

### Pearson Correlation

22. Problem 22 in Chapter 10 presented data showing that mature soccer players, who have a history of hitting soccer balls with their heads, had significantly lower cognitive scores than mature swimmers, who do not suffer repeated blows to the head. The independent-measures t test produced t = 2.11 with df = 11 and a value of r2

### Help Analyzing Correlations

I do not understand inferential statistics. I have attached a sample of some work that I have put together to help aide me in the process of understanding it. There are graphs that I have done in the SPSS software. I need help to understand how to read and analyze it.

### Pearson Correlation Assignment

Please look over what I have done and help me with the rest. My answers are in brackets. 2. What information is provided by the numerical value of the Pearson correlation? (The sample correlation coefficient, usually denoted r, is a numerical measure of the strength and the direction of the sample linear relationship betw

### Correlation and Hypothesis Testing

1. Using data consisting of diamond price and carat (weight) for thirty randomly selected diamonds, a correlation between price and weight was found to be 0.767. At the 0.01 level of significance, is there a positive association between the two variables? Show all 5 steps in the hypothesis testing process. 2. Kendra Korbi

### Data Analysis with SPSS

1.Use these data to answer question 1a and 1b. These are saved as Chapter 5 Date Set. Correct Attitude 17 94 13 73 12 59 15 80 16 93 14 85 16 66 16 79 18 77 19 91 a.Compute the Pearson product-moment correlation coefficient by hand and show all and show all your work. b.Construct a scatterplot for these 10 values b

### Using Pearson's correlation matrix

The United States is a diverse country; its criminal justice systems differ across its 50 states. As most criminal justice activity is organized at the local or state level, understanding American criminal justice often means understanding local and state differences. The data in "JUSTICE.SAV" will allow you to explore those soc

### Statistics: Determining Regression Coefficients

Please use data of the attached two tables to answer the following questions about Pb 9.24. C) Find the regression coefficiet a and b. K)iii. Construct the 99% confidence interval for ?. I)iii. Construct the 99% confidence interval for ?. (p) Compute the correlation coefficient r. q)ii. Construct the 95% confidence i

### Statistics: Pearson Correlation, Regression Equation

See attached file for tables. Problem Set 1: Chapter 16, problems 2, 6c, 14; Chapter 17, problem 14 2. What information is provided by the numerical value of the Pearson correlation? 6. For the following scores, X Y 1 5 2 9 4 3 5 1 3 2 c. Compute a Pearson Correlation 14. It is well known that similarity.

### Confidence Interval Population Correlations

Exercise 1 Following are measurements of tensile strength in ksi (x) and Brinell hardness (y) for 10 specimens of cold drawn copper. Assume that tensile strength and Brinell hardness follow a bivariate normal distribution. ______________________________________________ x y 106.2

### Hypothesis testing: Correlation Questions

1. When we have a straight-line relation between two variables, we use a Pearson correlation coefficient. What does this coefficient describe? 2. How are deviation scores used in assessing the relation between variables? 3. What are the null and research hypotheses for correlations? 4. Describe the third assumption of

### Compute and evaluate the Pearson correlation

Pearson correlation For the following set of scores, X Y 0 3 1 1 2 5 3 9 4 7 A. Compute the Pearson correlation. B. Multiply each X value by 2 and compu

### Correlation Coefficient between customer service attitude scores and overtime hours?

Using one of the two formulas cited in this module calculate the correlation coefficient using the following values presented below. Once you have completed your calculation, discussion the following: Is there a statistically significant correlation between customer service attitude scores and number of overtime hours? State the

### Correlation Coefficient random sample

Discuss the implications of: magnitude (from 0 to 1); sign ( + or -); and probability versus causality for the Correlation Coefficient (also known as the Pearson Product-Moment Correlation Coefficient). Describe how you would develop a random sample from among students.

### Methods of Establishing Correlation between Variables: Example

Describe different methods of establishing correlation between variables and provide an example of each. Discuss the advantages and disadvantages of each method and where each must be applied. Consider particular circumstances and examples in which a researcher may want to establish correlation.

### Methods of Establishing Correlation Between Variables

Describe different methods of establishing correlation between variables and provide an example of each. Discuss the advantages and disadvantages of each method and where each must be applied. Consider particular circumstances and examples in which a researcher may want to establish correlation.

### Pearson correlation; Regression equation; significant portion of the variance in the cognitive scores

2. What information is provided by the numerical value of the Pearson correlation? 6. for the following scores. ________ X Y ________ 1 5 2 9 4 3 5 1 3 2 (c ). Compare the Pearson Correlation. 14. It is well known that similarity in attitudes, believes and interests plays an important role in interpersona

### Correlation: Compute the Pearson correlation for political attitudes for married couples

It is well known that similarity in attitudes, beliefs, and interests plays an important role in interpersonal attraction (see Byrne, 1971, for example). Thus, correlations for attitudes between married couples should be strong. Suppose a researcher developed a questionnaire that measures how liberal or conservative one's attitu

### Important information about Pearson correlation

Correlation 1. What information is provided by the numerical value of the Pearson correlation? 2. For the following scores, compute the Pearson correlation: X Y 1 1 2 3 4 9 5 5 3 2 3. It is well known that similarity in attitudes, beliefs, and interests plays an important role in interpersonal attraction. Thus,

### Statistics: Compute the Pearson correlation

6. For the following scores: X Y 3 12 6 7 3 9 5 7 3 10 a. Compute the Pearson correlation. You should get -0.8333 according to my quick calculation. So, double check. b. With a small sample, a single point can have a large effect on the magnitude of the correlation. Change the score X = 5 to X = 0 and

### Significance of correlation coefficient.

Construct a scatter plot of the raw data. Then, run the correlation/regression program. New Car Mileage Ratings: Listed below are combined city-highway fuel economy ratings (in mi/gal) for different cars. The old ratings are based on tests used before 2008 and the new ratings are based on tests that went into effect in 2008.

### A Glimpse into History and Statistical Tests

Find historical information on the statisticians who developed statistical tests, such as the normal distribution, Student t distribution, Chi-Square distribution, F distribution, Mann-Whitney test, Pearson product-moment correlation, Spearman rank correlation, Wilcoxon nonparametric tests, Kruskal-Wallis test, Levene test, Ryan

### Statistics: Compute a Correlation Analysis Using the Statistical Functions in Excel.

Compute the correlation analysis using the statistical functions in Excel. A Pearson Product Movement Correlation Coefficient. See the attached file.

### Statistics

10.30 In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At &#945; = .01, did the yellow fire trucks have a signifi

### General Statistics

Factual questions (1 point each-10 points) No lengthy answers 1. Suppose that on a 100 item multiple choice test almost all students scored between 95 and 100 but a small scattering number of participants scored as low as 20.When plotted as a curve, the distribution will show what type of a curve? 2. If all participants in

X Y 90 10 86 9 94 7 70 6 86 7 90 15 94 10 66 5 98 11 86 9 1. Calculate and interpret the mean and standard deviation for variables X and Y. (5 points) 2. Calculate and interpret the Pearson's correlation coefficient between test scores (X) and number of hours a person studied for the te

### Explanation of Logic Behind the Sum of Products

Explanation on what is the logic behind using the sum of the products of deviation scores as the numerator of the formula for the correlation coefficient? Is this logic sound? Why or why not?

### Significance of correlation : T Test

An assumption for a significance test of the correlation coefficient is that the populations, the variance of each variable is the same at each point of the other variable. Are there other assumptions to correlation coefficient? What happens if these assumptions are not met? What two numbers do you need to figure the t score f

### Pearson correlation

What information is provided by the numerical value of the Pearson correlation?