Brief Answers Needed ASAP In One Or Two Hours

Brief Answers Need Asap In One Or 2 Hour1 A In Your Own Words Wha

1) a) In your own words, what is spurious correlation? b) What is the definition of spurious correlation and cite where you got it from (don’t use the slides). c) In your own words, what is reverse causality? d) What is the definition of reverse causality and cite where you got it from (don’t use the slides). e) What is R^2 in your own words? f) What is the exact definition from our slides? (or the one I say in class). g) From our slides, repeat the six comments about R^2 in your own words (don’t copy and paste).

2) a) Give two different reasons why you would want to run a regression through the origin. b) give two cases where regression through the origin might be reasonable that are not in our slides on the subject. c) How do we safely determine if we should include an intercept term or not?

Paper For Above instruction

Spurious correlation refers to a statistical relationship between two variables that appears significant but is actually caused by an external factor or coincidence rather than a direct causal link. It can mislead analysts into believing there is a meaningful association when, in reality, the variables are unrelated. For example, the number of films Nicolas Cage appears in and the number of people who drown in swimming pools might be correlated over some period, but this does not imply causation; both are influenced by unrelated external factors like population growth or time trends.

The formal definition of spurious correlation, as described in statistical literature, is a high correlation between two variables that arises due to the influence of a third variable, such as time trends or seasonal effects, without any real causal connection. This term is often associated with studies where variables seem related statistically, but upon closer examination, the relationship is confounded by external influences. According to Greene (2012), spurious correlation occurs when the correlation coefficient is high in the presence of such confounding factors, misleading researchers about the true relationship.

Reverse causality occurs when the direction of cause-and-effect between two variables is opposite to what is assumed or intended. Instead of variable X causing variable Y, it is actually Y that influences X. For example, while one might assume that increased advertising causes higher sales, it could be that higher sales enable a company to invest more in advertising, thus reversing the causality. Reverse causality can lead to incorrect conclusions in regression analysis if not properly identified or controlled for.

According to our class slides, reverse causality is defined as a situation where the causative relationship between variables runs in the opposite direction of what is initially assumed, leading to potential bias in estimating causal effects. It is a common challenge in observational studies when the temporal order of cause and effect cannot be definitively established.

R-squared, or R^2, is a statistical measure that indicates the proportion of variance in the dependent variable that can be explained by the independent variables in a regression model. In simple terms, it shows how well the model fits the data; an R^2 of 0.8 suggests that 80% of the variability in the outcome is explained by the predictors.

From our slides, R^2 is exactly defined as the coefficient of determination, which quantifies the proportion of the total variation in the dependent variable that is explained by the independent variables in the model. It ranges from 0 to 1, with higher values indicating a better fit.

The six comments about R^2 from our slides, paraphrased, are as follows: First, R^2 measures the goodness-of-fit of the model; second, a high R^2 does not necessarily mean the model is appropriate or causal; third, adding more variables can increase R^2 even if they are not relevant; fourth, R^2 values are more useful for comparing models than for establishing causality; fifth, a low R^2 indicates a poor fit, but the model may still be useful for inference; sixth, R^2 alone should not be used as the sole criterion for model selection.

Reasons for running a regression through the origin include theoretical considerations where the relationship logically starts at zero, and to simplify models when the intercept is not meaningful or its inclusion complicates interpretation. For example, in physics, if the force applied is zero, the resulting acceleration should also be zero, justifying regression through the origin.

Two cases where regression through the origin might be reasonable outside the slides could include measuring manufacturing defects where the baseline defect rate is known to be zero, or when studying the cost of a service that incurs no cost if no units are produced or consumed. In such cases, forcing the intercept to zero aligns with the underlying theory or operational conditions.

To safely determine whether to include an intercept, we can perform statistical tests such as the F-test or t-test to compare models with and without the intercept. Analyzing residual plots and considering theoretical justification are also important. If the intercept is statistically indistinguishable from zero and theory supports a zero intercept, then running a regression through the origin may be appropriate.

References

• Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson.
• Wooldridge, J. M. (2013). Introductory Econometrics: A Modern Approach (5th ed.). South-Western College Pub.
• Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). McGraw-Hill/Irwin.
• Stock, J. H., & Watson, M. W. (2015). Introduction to Econometrics (3rd ed.). Pearson.
• Allison, P. D. (2012). Regression and Other Topics in Life Cycle Data Analysis. SAGE Publishing.
• Baldi, P., & Sadowski, P. J. (2014). An Introduction to Modern Econometrics. Wiley.
• Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics. Princeton University Press.
• Kennedy, P. (2008). A Guide to Econometrics (6th ed.). Wiley.
• Maddala, G. S., & Lahiri, K. (2009). Introduction to Econometrics. Wiley.
• Stock, J. H., & Watson, M. W. (2019). Modeling and Analysis of Time Series Data. Pearson.