If the correlation coefficient is a positive value, then the slope of the regression line

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If the coefficient of correlation is -0.4, then the slope of the regression line, A. must be 0.16 B. can be either negative or positive C. must be also -0.4 D. must be negative

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In this problem, the and so forth. At this age, the obscenity must be negative much to be negative. It is because it is because coefficient of correlation, coefficient of coefficient of poor relation and slope off the and slow of the integration and slope of the regression line is directly line needs directly proportional to each other, proportional so eat. I did Both are the same sign and it may or may not possible to get the same value of correlation and slope. So it's sensory. The option D. That is coefficient of correlation of co Relation 8 -14. Then the slope of the regulation line must be negative.

Week 10 answer key:QuestionAnswer1c2a3d4c5aWEEK 111)If we wish to test that each independent variable makes a contribution to a multiple regressionmodel, we conduct a:a)T-testb)F-Testc)Both of the aboved)None of the above as there is insufficient information

2)Assume that F significance value in a multiple linear regression output is 2.05E-06. At the 5%level of significance, this means that

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3)The significance level of a test on the slope of a simple linear regression equation measures theprobability of drawing an incorrect conclusion when the test indicates that X and Y have asignificant relationship

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4)Coefficient of determination tells us

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If the coefficient of correlation is a positive value, then the slope of the regression line: a. must also be positive. b. can be either negative or positive. c. can be zero. d. None of the above answers is correct.

Answer to: If the coefficient of correlation is a positive value, then the slope of the regression line: a. must also be positive. b. can be either negative...

Simple linear regression

If the coefficient of correlation is a positive value, then the slope of the regression line: a.... Question:

1. If the coefficient of correlation is a positive value, then the slope of the regression line:

A. must also be positive.

B. can be either negative or positive.

C. can be zero.

D. None of the above answers is correct.

Correlation Coefficient:

Linear regression analysis is a statistical procedure done to determine the strength of the relationship between two quantitative variables that are linearly related. The value of the correlation coefficient gives the strength of the relationship denoted as

r r . The values of r r range from − 1 −1

to 1. The nearer the value of

r r

to 1, the higher the correlation. When the value of

r r

gets closer to 0, the weaker is the relationship between them. However, the value of

r r

does not tell us about the change in the dependent variable that corresponds to every unit change in the independent variable.

Answer and Explanation:

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1. The answer is A. must also be positive.

The independent variable is often referred to as the predictor variable in a linear regression analysis,...

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Simple Linear Regression: Definition, Formula & Examples

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Simple linear regression refers to the relationship between two variables. Learn the definition of simple linear regression, understand how to use the scatterplot and formula to find the regression line by hand or graphing calculator, and review the examples.

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What is the difference between correlation and linear regression?

KNOWLEDGEBASE - ARTICLE #1141

What is the difference between correlation and linear regression?

Last modified October 3, 2019

When investigating the relationship between two or more numeric variables, it is important to know the difference between correlation and regression. The similarities/differences and advantages/disadvantages of these tools are discussed here along with examples of each.

Correlation quantifies the direction and strength of the relationship between two numeric variables, X and Y, and always lies between -1.0 and 1.0. Simple linear regression relates X to Y through an equation of the form Y = a + bX.

Key similarities 

Both quantify the direction and strength of the relationship between two numeric variables.

When the correlation (r) is negative, the regression slope (b) will be negative.

When the correlation is positive, the regression slope will be positive.

The correlation squared (r2 or R2) has special meaning in simple linear regression. It represents the proportion of variation in Y explained by X.

Key differences 

Regression attempts to establish how X causes Y to change and the results of the analysis will change if X and Y are swapped. With correlation, the X and Y variables are interchangeable.

Regression assumes X is fixed with no error, such as a dose amount or temperature setting. With correlation, X and Y are typically both random variables*, such as height and weight or blood pressure and heart rate.

Correlation is a single statistic, whereas regression produces an entire equation.

Prism helps you save time and make more appropriate analysis choices. Try Prism for free.

*The X variable can be fixed with correlation, but confidence intervals and statistical tests are no longer appropriate. Typically, regression is used when X is fixed.

Learn more about correlation vs regression analysis with this video by 365 Data Science

Key advantage of correlation

Correlation is a more concise (single value) summary of the relationship between two variables than regression. In result, many pairwise correlations can be viewed together at the same time in one table.

Key advantage of regression

Regression provides a more detailed analysis which includes an equation which can be used for prediction and/or optimization.

Correlation Example

As an example, let’s go through the Prism tutorial on correlation matrix which contains an automotive dataset with Cost in USD, MPG, Horsepower, and Weight in Pounds as the variables. Instead of just looking at the correlation between one X and one Y, we can generate all pairwise correlations using Prism’s correlation matrix. If you don’t have access to Prism, download the free 30 day trial here. These are the steps in Prism:

Open Prism and select Multiple Variables from the left side panel.

Choose Start with sample data to follow a tutorial and select Correlation matrix.

Click Create. Click Analyze.

Select Multiple variable analyses > Correlation matrix.

Click OK twice.

On the left side panel, double click on the graph titled Pearson r: Correlation of Data 1.

The Prism correlation matrix displays all the pairwise correlations for this set of variables.

The red boxes represent variables that have a negative relationship.

The blue boxes represent variables that have a positive relationship

The darker the box, the closer the correlation is to negative or positive 1.

Ignore the dark blue diagonal boxes since they will always have a correlation of 1.00.

Key findings: 

Horsepower and MPG have a strong negative relationship (r = -0.74), higher horsepower cars have lower MPG.

Horsepower and cost have a strong positive relationship (r = 0.88), higher horsepower cars cost more.

Note that the matrix is symmetric. For example, the correlation between “weight in pounds” and “cost in USD” in the lower left corner (0.52) is the same as the correlation between “cost in USD” and “weight in pounds” in the upper right corner (0.52). This reinforces the fact that X and Y are interchangeable with regard to correlation. The correlations along the diagonal will always be 1.00 and a variable is always perfectly correlated with itself.

When interpreting correlations, you should be aware of the four possible explanations for a strong correlation:

Changes in the X variable causes a change the value of the Y variable.

Changes in the Y variable causes a change the value of the X variable.

Changes in another variable influence both X and Y.

X and Y don’t really correlate at all, and you just happened to observe such a strong correlation by chance. The P value quantifies the likelihood that this could occur.

Regression Example

The strength of UV rays varies by latitude. The higher the latitude, the less exposure to the sun, which corresponds to a lower skin cancer risk. So where you live can have an impact on your skin cancer risk. Two variables, cancer mortality rate and latitude, were entered into Prism’s XY table. The Prism graph (right) shows the relationship between skin cancer mortality rate (Y) and latitude at the center of a state (X). It makes sense to compute the correlation between these variables, but taking it a step further, let’s perform a regression analysis and get a predictive equation.

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Slope of Regression Line and Correlation Coefficient

Discover how the slope of the regression line is directly dependent on the value of the correlation coefficient r.

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The Slope of the Regression Line and the Correlation Coefficient

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Updated on February 06, 2020

Many times in the study of statistics it is important to make connections between different topics. We will see an example of this in which the slope of the regression line is directly related to the correlation coefficient. Since these concepts both involve straight lines, it is only natural to ask the question, "How are the correlation coefficient and least square line related?"

First, we will look at some background regarding both of these topics.

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Details Regarding Correlation

It is important to remember the details pertaining to the correlation coefficient, which is denoted by r. This statistic is used when we have paired quantitative data. From a scatterplot of paired data, we can look for trends in the overall distribution of data. Some paired data exhibits a linear or straight-line pattern. But in practice, the data never falls exactly along a straight line.

Several people looking at the same scatterplot of paired data would disagree on how close it was to showing an overall linear trend. After all, our criteria for this may be somewhat subjective. The scale that we use could also affect our perception of the data. For these reasons and more we need some kind of objective measure to tell how close our paired data is to being linear. The correlation coefficient achieves this for us.

A few basic facts about r include:

The value of r ranges between any real number from -1 to 1.

Values of r close to 0 imply that there is little to no linear relationship between the data.

Values of r close to 1 imply that there is a positive linear relationship between the data. This means that as x increases that y also increases.

Values of r close to -1 imply that there is a negative linear relationship between the data. This means that as x increases that y decreases.

The Slope of the Least Squares Line

The last two items in the above list point us toward the slope of the least squares line of best fit. Recall that the slope of a line is a measurement of how many units it goes up or down for every unit we move to the right. Sometimes this is stated as the rise of the line divided by the run, or the change in y values divided by the change in x values.

In general, straight lines have slopes that are positive, negative, or zero. If we were to examine our least-square regression lines and compare the corresponding values of r, we would notice that every time our data has a negative correlation coefficient, the slope of the regression line is negative. Similarly, for every time that we have a positive correlation coefficient, the slope of the regression line is positive.

It should be evident from this observation that there is definitely a connection between the sign of the correlation coefficient and the slope of the least squares line. It remains to explain why this is true.

The Formula for the Slope

The reason for the connection between the value of r and the slope of the least squares line has to do with the formula that gives us the slope of this line. For paired data (x,y) we denote the standard deviation of the x data by sx and the standard deviation of the y data by sy.

The formula for the slope a of the regression line is:

a = r(sy/sx)

The calculation of a standard deviation involves taking the positive square root of a nonnegative number. As a result, both standard deviations in the formula for the slope must be nonnegative. If we assume that there is some variation in our data, we will be able to disregard the possibility that either of these standard deviations is zero. Therefore the sign of the correlation coefficient will be the same as the sign of the slope of the regression line.

स्रोत : www.thoughtco.com

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