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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

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

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.

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,

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


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 α = .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

Hypothesis about Correlation Coefficient

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

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

Correlational Research

Briefly describe correlational research. Name a variable from this study and one from the workplace that might prove to provide a correlational relationship and explain why you would choose these two? What did you learn about correlation and causation?

Testing of significance of correlation coefficient

I know the answer for the following problem is : r=-0.69, df=10, not significant at 0.5 How do I get to that answer? An economist is interested in studying the relationships between length of unemployment and job seeking activity among white collar workers. He interviews a sample of 12 unemployment accountants as to th

Testing of hypothesis, Interpreataion of linear correlation

1. When using the F-statistic for hypothesis testing of the variance, which sample variance is the numerator and which sample variance is the denominator? 2. How do you interpret the linear correlation coefficient? 3. How do you test the equality of population variances? 4.How do you test the significant differences bet

1. Use the data to construct a scatter plot, then test for a linear correlation between pain intensity before and after the treatment. If there is a significant linear correlation, does it follow that the drug treatment is effective? 2. Find the equation of the regression line. Let the response (y) variable be the pain intensity after the treatment. What would be the equation of the regression line for a treatment having absolutely no effect?

Listed below are measures of pain intensity before and after using the proprietary drug Duragesic. The data are listed in order by row, and corresponding measures are from the same subject before and after the treatment. For example, the first subject had a measure of 1.2 before the treatment and a measure of 0.4 after the t

Correlation: Calculate and interpret the correlation between variables.

The product development team at Piggybank is wondering if there is a correlation between retail online sales and total retail sales, so calculate the correlation between online and total retail sales, and interpret the results. If your peers are struggling with the calculations, share examples and insights to help them along. Gi

Hypothesis testing using T-test, correlation

1. A teacher wants to describe the results of a particular test. The test grades were 88,78,79,69,83,82,90,94,95,87,85,83,88,89,90,65,76,88,62,90. What would be and how would you find the mean, median, mode, range, variance, standard deviation, an ordered array, a stem-and leaf, a box-and-whiskers and a bar chart of the class sc

Correlation Coefficient Calculated

1 (a) The following data was obtained for two variables, X & Y X 135 110 130 145 175 160 120 Y 145 100 120 120 130 130 110 (i) Plot a scatter diagram for this data (ii) Calculate the Pearson product moment correlation coefficient and the regression coefficients for this data (iii) This data set seems to contain an out

The reliability coefficient is examined.

The reliability coefficient is maximized when: a) The examinees are heterogeneous b) the examiners are homogeneous c) THe examinees are very similar d) Both b abd c are correct Answers are explained below.