According to a machine-learning expert, linear regression

According to a machine-learning expert, linear regression models are useless because they miss logarithmic, polynomial, sinusoidal and other non-linear patterns.

  1. If in a regression of y on x you obtain a slope of β, then in a regression of x on y (switching them in the roles of dependent and independent variables) the resulting slope must be 1/β.
  2. Including a dummy for gender as an explanatory variable in a regression is one way to allow for heterogeneity in our estimates.
  3. Running a regression requires the dependent variable to be distributed normal. In contrast, the independent variables can have any distribution.
  4. If we could draw many random samples from the same population, and each time we ran the exact same regression, then we would get different regression coefficients but the same standard errors.
  5. In a regression, the standard error of an estimate is itself an estimate.
  6. Two analytics teams within a company tried to estimate the same parameter running the same regression. Their estimates were identical. However, the p-value was 0.016 in one study and 0.027 in the other. We can be sure that the difference in p-values is due to sample size differences.
  7. If the 95% confidence interval of a regression coefficient is (0.23,0.72) then the true parameter is above 0.72 with probability 0.025 and below 0.23 with probability 0.025.
  8. An analyst omitted a variable in a regression. She is sure that, since the omitted variable is positively correlated with all the regressors, the resulting βs are overestimated.
  9. Assume a regression coefficient has a p-value of 0.02. Then, at 95% confidence we reject the hypothesis that the true parameter is zero. However, at 99% confidence we accept the same hypothesis.
  10. Answer true/false/uncertain and explain your answer. The grade depends on your explanation. You can use charts and equations to support your answers. However, explanations with words are required. 

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