An explanation for Q-2 &3 would be appreciated.
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Hi,
1. For question 2, since R^2 = 0.80, it means that 80% of the variation in y i.e. the dependent variable is explained by x i.e. the independent variable. RSS i.e. Regression sum of squares basically tells us about the explained variation and ESS i.e. Error sum of squares tells us about the unexplained variation in y. Now since R^2 exceeds 0.5, therefore it means RSS will be greater than ESS. This is what we can imply from the equation.
2. For question 3, you know that we test conditional heteroskedasticity using Breusch Pagan Test i.e. (BP) test. In this test we carry out a regression between the error term and all the independent variables to check for conditional heteroskedasticity (i.e. if the variance of error term is changing in a pattern with the independent variable). Therefore, in this we take Hypothesis as:
H0: BP = 0 (i.e. No conditional Heteroskedasticity)
H1: BP <>0 (i.e. Conditional Heteroskedasticity present)
We want R^2 from this Regression to be low and in the end we want to accept i.e. fail to reject H0.
Conclusion: Therefore, Sawyer is likely to conclude that her regression does not exhibit conditional Heteroskedasticity when R^2 is close to 0.
Hope this helps!