Actually, is there a relationship in regression when changing values?

In summary, the speaker is discussing their confusion about the results of a regression problem where the x and y values were swapped. They expected the regression values to be inverses, but they were not. The speaker also mentions that they do not fully understand regression and asks for an explanation. Another speaker responds by pointing out that there is no simple relationship between the coefficients obtained in the two regressions, and suggests looking at the formula for slope when regressing y on x. They also mention that switching the roles of the two variables gives a different formula for the slope when regressing x on y.
  • #1
Soley101
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Hello, I've just started learning about regression. While working on some problems I noticed that one problem set had exactly the x,y values swapped. And as you know when you switch the points that's normally an inverse, but the regression doesn't show that pattern as the regression values are not inverses. I expected them to be the inverses but they are not. How do I explain that..maybe I don't fully understand what regression is.

For instance (I don't have my calc on me but I assure you I know how to do the regression) but I am mean let's say there are 3 coordinates 2,2 3,4 6,6 then the reverse would be 2,2 4,3 6,6. But the regressions are not identical. so is there a pattern or relationship? lol i go crazy at this hour.
 
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  • #2
There is no simple relationship between the coefficients obtained in the two regressions. Look at the formula for slope when you regress [tex] y [/tex] on [tex] x [/tex]. Switching the roles of the two variables gives the formula for the ''slope'' when you regress [tex] x [/tex] on [tex] y [/tex].
 

1. What is regression analysis and how is it used in scientific research?

Regression analysis is a statistical technique used to analyze the relationship between a dependent variable and one or more independent variables. It is commonly used in scientific research to understand the effect of different variables on a particular outcome or to make predictions based on historical data.

2. How do you determine if there is a relationship in regression when changing values?

The strength and direction of the relationship in regression can be determined by calculating the correlation coefficient, also known as r. A positive value of r indicates a positive relationship, whereas a negative value indicates a negative relationship. The closer r is to 1 or -1, the stronger the relationship. A value close to 0 indicates little to no relationship.

3. Can regression analysis determine causation?

No, regression analysis can only show a relationship between variables, but it cannot determine causation. In order to establish causation, additional research and experiments are needed.

4. How do you interpret the results of a regression analysis?

The results of a regression analysis typically include the coefficient of determination (R-squared), which represents the percentage of variation in the dependent variable that can be explained by the independent variable(s). Additionally, the regression equation, which shows the relationship between the variables, can be used to make predictions or draw conclusions about the data.

5. What are some common pitfalls to avoid when conducting regression analysis?

Some common pitfalls to avoid when conducting regression analysis include not using enough data points, assuming a linear relationship when there may be a curved or nonlinear relationship, and not considering other variables that may be influencing the outcome. It is also important to avoid making assumptions about causation based on correlation and to properly interpret the results in the context of the research question.

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