Find Regression Equation for y on x

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In summary, the conversation discusses the difficulty of determining a regression equation without any data context or information. The question posed is impossible to answer without additional information such as a graph or table of data. The concept of using the regression coefficient and the range of r is also mentioned, but without any data, it cannot be applied.
  • #1
Doffy
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How do I determine the regression equation when not much information is given? For example:
Given the following equations:
2x + y = 13
2x + 5y = 20,

which one is the regression equation of y on x?
 
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  • #2
Regression equations only make sense in the context of data that you're trying to explain using some model. Your question is quite impossible to answer unless there is some data present. Were you given, say, a graph of some data? Or a table of data?
 
  • #3
Ackbach said:
Regression equations only make sense in the context of data that you're trying to explain using some model. Your question is quite impossible to answer unless there is some data present. Were you given, say, a graph of some data? Or a table of data?

Well, I am afraid that no further information of any kind is available.
However, I was wondering that since regression coefficient is the geometric mean of the regression coefficients, can we use this fact to determine our equation?
Also that, the range of r is -1\(\displaystyle \le\) r \(\displaystyle \le\) +1. Is it possible?
 
  • #4
We have no regression coefficients, we have no context. Your question is completely impossible to answer as is, I'm afraid. Both linear equations you've given could easily be the best fit line for a particular data set; but without that data set, there's no way to tell which line would fit the data better.
 

1. What is a regression equation for y on x?

A regression equation for y on x is a mathematical formula that allows you to predict the value of the dependent variable (y) based on the value of the independent variable (x). It is commonly used in data analysis to determine the relationship between two variables and make predictions based on that relationship.

2. How do you find a regression equation for y on x?

To find a regression equation for y on x, you need to first plot the data points on a graph and determine if there is a linear relationship between the two variables. If there is, you can use a statistical method such as the least squares method to calculate the slope and intercept of the regression line. These values can then be used to create the regression equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

3. What is the purpose of finding a regression equation for y on x?

The purpose of finding a regression equation for y on x is to understand the relationship between two variables and make predictions based on that relationship. It can also help in identifying any trends or patterns in the data and can be used to make informed decisions in various fields such as economics, psychology, and science.

4. What are the limitations of using a regression equation for y on x?

One limitation of using a regression equation for y on x is that it assumes a linear relationship between the two variables. If the relationship is non-linear, the regression equation may not accurately represent the data. Additionally, it is important to note that correlation does not imply causation, so a regression equation may not always provide a causal explanation for the relationship between two variables.

5. What are some common applications of using a regression equation for y on x?

A regression equation for y on x is commonly used in fields such as economics, finance, psychology, and social sciences to predict and analyze various phenomena. Some specific applications include predicting stock prices, analyzing consumer behavior, and understanding the impact of certain factors on human health and behavior.

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