Suppose you are interested in estimating the impact of different inputs (temperature, rainfall, fertilizer) on agricultural crop yields. Your unit of analysis is farm-level. In writing the organic carbon soil content (soil quality, essentially). However, you cannot find data on soil quality when you go to estimate the equation. Write out your theoretical regression eq a result of not having data on soil quality? Specifically, show how you determine whether your estimates are upper or lower bounds of the true estimates of the impact of fertilizer
Suppose you are interested in estimating the impact of different inputs (temperature, rainfall, fertilizer) on agricultural crop yields. Your unit of analysis is farm-level. In writing the organic carbon soil content (soil quality, essentially). However, you cannot find data on soil quality when you go to estimate the equation. Write out your theoretical regression eq a result of not having data on soil quality? Specifically, show how you determine whether your estimates are upper or lower bounds of the true estimates of the impact of fertilizer
Chapter4: Linear Functions
Section: Chapter Questions
Problem 8PT: Does Table 1 represent a linear function? If so, finda linear equation that models the data.
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Question
![Suppose you are interested in estimating the impact of different inputs (temperature, rainfall, fertilizer) on agricultural crop yields. Your unit of analysis is farm-level. In writing the structural regression equation, you want to control for the organic carbon soil content (soil quality, essentially). However, you cannot find data on soil quality when you go to estimate the equation. Write out your theoretical regression equation and the estimated regression equation. What happens as a result of not having data on soil quality? Specifically, show how you determine whether your estimates are upper or lower bounds of the true estimates of the impact of fertilizer.
**Theoretical:**
\[ Y = \beta_0 + \beta_1T + \beta_2R + \beta_3F + \beta_4S + \varepsilon \]
**Estimated:**
\[ Y = \hat{\beta}_0 + \hat{\beta}_1T + \hat{\beta}_2R + \hat{\beta}_3F \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12329165-83a7-4f90-ae4e-cd06099490e5%2Fb90db1aa-c63f-462c-a16c-b8ae3955bd86%2Ffx0ylf_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose you are interested in estimating the impact of different inputs (temperature, rainfall, fertilizer) on agricultural crop yields. Your unit of analysis is farm-level. In writing the structural regression equation, you want to control for the organic carbon soil content (soil quality, essentially). However, you cannot find data on soil quality when you go to estimate the equation. Write out your theoretical regression equation and the estimated regression equation. What happens as a result of not having data on soil quality? Specifically, show how you determine whether your estimates are upper or lower bounds of the true estimates of the impact of fertilizer.
**Theoretical:**
\[ Y = \beta_0 + \beta_1T + \beta_2R + \beta_3F + \beta_4S + \varepsilon \]
**Estimated:**
\[ Y = \hat{\beta}_0 + \hat{\beta}_1T + \hat{\beta}_2R + \hat{\beta}_3F \]
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