R-Squared Difference when Dependent variable is $/lb vs Total Dollars?

In summary, the speaker is asking why there is a significant difference in the r-square values (98.5% vs 85%) when changing the dependent variable from Total $'s to $'s per lb, while the independent variable remains weight. They mention that both equations yield essentially the same answer for all tests of weight. They are unsure which variable best represents their data and are concerned about the impact on management when explaining the variation in price. To illustrate, they provide an example of a part that weighs 2 pounds, with the Total dollars equation estimating $72.645 and the $/lb equation estimating $36.33/lb (which equals $72.66 for 2 pounds). They state that this pattern holds
  • #1
stats1322
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Why would I see a fairly significant difference in r-square (98.5% vs 85%) when I change my dependent variable from Total $'s to $'s per lb? My independent variable in both cases is weight. Each equation yields essentially the same answer in all tests of weight (within .08%).

How do I know which one best represents my data? It makes a difference when talking to management if something explains all but 1.5% of the variation in price, vs 15%.
 
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  • #2
Example of the difference...

A part that weighs 2 pounds:
Total dollars equation estimates $72.645
$/lb equation estimates $36.33/lb (36.33*2 = $72.66)

This is how it looks for all the different parts.
 
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1. What is the significance of R-squared difference when the dependent variable is $/lb vs Total Dollars?

The R-squared difference is a statistical measure that indicates the proportion of variation in the dependent variable (total dollars) that can be explained by the independent variable ($/lb). In other words, it shows how well the independent variable explains the changes in the dependent variable. A higher R-squared difference indicates a stronger relationship between the variables.

2. How is R-squared difference calculated?

R-squared difference is calculated by taking the difference between the R-squared values of two regression models. The first model uses $/lb as the independent variable and the second model uses total dollars as the independent variable. The formula for R-squared difference is: R-squared difference = R-squared value of model 1 - R-squared value of model 2.

3. Can R-squared difference be negative?

Yes, R-squared difference can be negative. This means that the second model (with total dollars as the independent variable) has a higher R-squared value than the first model (with $/lb as the independent variable). A negative R-squared difference may indicate that the independent variable is not a good predictor of the dependent variable.

4. What is a good R-squared difference?

The interpretation of a good R-squared difference depends on the specific context and research question. In general, a higher R-squared difference is desirable as it indicates a stronger relationship between the variables. However, it is important to also consider the overall fit and significance of the regression models, and not solely rely on the R-squared difference to evaluate the models.

5. How can R-squared difference be used in data analysis?

R-squared difference can be used to compare the explanatory power of different independent variables in a regression model. It can also be used to determine which independent variable is a better predictor of the dependent variable. Additionally, R-squared difference can be used to assess the impact of adding or removing a variable from a regression model. However, it is important to note that R-squared difference should not be the sole determinant in model selection and other factors, such as the theoretical significance of the variables, should also be considered.

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