Coefficient of determination

In summary, the coefficient of determination, also known as R-squared, is a statistical measure that indicates the proportion of the variance in the dependent variable that is explained by the independent variable(s). It is calculated by squaring the correlation coefficient (r) between the two variables and is a value between 0 and 1, with higher values indicating a stronger relationship. A good value for the coefficient of determination depends on the context and field of study, with values above 0.7 considered strong and values below 0.3 considered weak. Adjusted R-squared is a modified version that takes into account the number of independent variables and is a more reliable measure of the relationship. The coefficient of determination cannot be negative, as it is
  • #1
adeel
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Ive been posting many questions, hopefully the alst for awhile:

You have collected data on sales and population within a one mile radius on 12 stores of a supermarket. You determined that the adjusted coefficient of determination is 93.85%. Determine the coefficient of determination.


I think there sitn enough info, but I guess I could be missing something.
 
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  • #2
sorry, did i post in the wrong section
 
  • #3


Hi there,

The coefficient of determination, also known as R-squared, is a statistical measure that indicates the percentage of variation in the dependent variable (sales) that can be explained by the independent variable (population). It ranges from 0 to 1, with 1 being a perfect fit.

In this case, the adjusted coefficient of determination is 93.85%, which means that 93.85% of the variation in sales can be explained by the population within a one mile radius. This is a high value, suggesting a strong relationship between sales and population.

To determine the coefficient of determination, we would need to know the actual value of R-squared. However, without the raw data, it is not possible to calculate it. I would suggest double-checking your question to see if there is any additional information that can help us determine the coefficient of determination.

I hope this helps. Best of luck with your research!
 

What is the coefficient of determination?

The coefficient of determination, also known as R-squared, is a statistical measure that indicates the proportion of the variance in the dependent variable that is explained by the independent variable(s). It is a value between 0 and 1, with higher values indicating a stronger relationship between the variables.

How is the coefficient of determination calculated?

The coefficient of determination is calculated by squaring the correlation coefficient (r) between the two variables. This can be done using a statistical software or by hand using a formula. It is important to note that the coefficient of determination only measures the strength of the linear relationship between the variables.

What is a good value for the coefficient of determination?

A good value for the coefficient of determination depends on the context and the field of study. In general, a value above 0.7 is considered a strong relationship, while a value below 0.3 is considered a weak relationship. However, it is important to interpret the coefficient of determination in conjunction with other statistical measures and the research question at hand.

What is the difference between adjusted R-squared and R-squared?

Adjusted R-squared is a modified version of R-squared that takes into account the number of independent variables in the model. Unlike R-squared, which will always increase with the addition of more variables, adjusted R-squared can decrease if the added variable does not significantly improve the model. This makes it a more reliable measure of the strength of the relationship between the variables.

Can the coefficient of determination be negative?

No, the coefficient of determination cannot be negative. It is a squared value, so it will always be positive. If the calculated value is negative, it is likely due to an error in the calculation or interpretation of the data.

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