Use the csv file Fish.csv (download at https://www.kaggle.com/aungpyaeap/fish-market) to answer the questions below. In this file,

• Species is the fish specimen's species,
• Weight is the specimen's weight in grams,
• Length1 is the specimen's "vertical" length in cm,
• Length2 is the specimen's "diagonal" length in cm,
• Length3 is the specimen's "cross" length in cm,
• Height is the specimen's height in cm,
• Width is the specimen's width in cm.

The measurements were made for 159 specimens.

1. Run the OLS linear regression (to estimate the coefficients) as given below. Report the estimated equation, the R2 and the adjusted R2. Attach your R code. (1)

i = 0 + 1Length1i (*)

2. Run the OLS linear regression (to estimate the coefficients) as given below. Report the estimated equation, the R2 and the adjusted R2. Attach your R code. (1)

i = 0 + 1Length1i + 2Length2i (**) 2

3. Run the OLS linear regression (to estimate the coefficients) as given below. Report the estimated equation, the R2 and the adjusted R2. Attach your R code. (1)

i = 0 + 1Length1i + 2Length2i + 3Length3i (***)

4. Run the OLS linear regression (to estimate the coefficients) as given below. Report the estimated equation, the R2 and the adjusted R2. Attach your R code. (1)

i = 0 + 1Length1i + 4Heighti (****)

5. Run the OLS linear regression (to estimate the coefficients) as given below. Report the estimated equation, the R2 and the adjusted R2. Attach your R code. (1)

i = 0 + 1Length1i + 2Length2i + 3Length3i + 4Heighti + 5Widthi + [whatever you need to add to the equation in order to control for the species] (*****)

6. Which of the models above [(*), (**), (***), (****), or (*****)] would you say is the best of the five? Explain why. (2)

7. Explain, in your own words, why the estimated slope coefficient 1 is not the same in all your equations (why you get a different number for the estimated slope even though you use the same data for every model). (1)

8. Create and test hypotheses for all the slope coefficients in the last (*****) equation, at the 5-percent significance level. Show your work. (1)

9. Test the overall significance of the last equation with the F-test at the 5-percent significance level. Show your work. (1)