Multiple Regression Analysis Assignment

Please answer the following questions based on the four videos.

Multiple Regression Part 1: The Very Basics

https://www.youtube.com/watch?v=dQNpSa-bq4M

1. Why do we need Multiple Regression?
2. What are the two Predictor variables in the example in the video? What is the response variable?
3. Multiple regression is an ________ of simple linear regression.
4. What is OVERFITTING?
5. What is MULTICOLLINEARITY?
6. What is the formula for the Multiple Regression Model?
7. What is the formula for the Multiple Regression Equation?
8. What is the formula for the Estimated Multiple Regression Equation?
9. Complete the statement: In multiple regression, each coefficient is interpreted as ...

Multiple Regression Part 2: Preparation

https://www.youtube.com/watch?v=2I_AYIECCOQ

1. What are the steps required before running a multiple regression?
2. What should you do if an independent variable is not correlated to a dependent variable prior to conducting the multiple regression analysis?
3. What are we looking for when constructing scatterplots between each of the independent variables?
4. What happens if two variables are REDUNDANT?
5. What is the use of the P-Value in determining correlation and significance between two independent variables?
6. What is the requirement of the r values and P-values when comparing independent variables with the dependent variables?
7. If two independent variables are highly correlated with an r value close to 1, what should you do with two variables?

Multiple Regression Part 3A: Evaluating Basic Models

https://youtu.be/wPJ1_Z8b0wk?t=120 (skip the first 2 minutes, start at 2:00)

1. What is the Standard Error of the Regression?
2. What is the mathematical meaning of the 3.18556 and the 0.0403 in the first simple regression?
3. The author uses a prediction interval after calculating the first simple regression equation between travel time and miles traveled. What does that prediction interval give us? Meaning, what's the point of doing that calculation?
4. The video mentions something called F-Value. We have not covered that. Look up F-value and find a simple explanation of what that is.
5. What is the R-squared if the two variables do not have a correlation?
6. What does it mean if the standard error of the regression model is smaller?

Multiple Regression Part 3B: Multiple Regression, Evaluating Basic Models

https://www.youtube.com/watch?v=px72eCYPuvc

1. In the first example of multiple regression, neither of the two variable are significant.Why did that happen?
2. What is the Variance Inflation Factor (VIF)? What does it help us find? If the VIF goes above what number does it mean the coefficients are poorly estimated?
3. What does it mean if there is a negative coefficient in the multiple regression model? In this example, does it make sense? Why or why not?
4. Why did the video eliminate all of the two and three variable options?
5. Which model was the best model and why?
6. What number was the highest in the best model?
7. What does the large drop off from the R-squared adjusted to the R-squared predicted indicate?
8. What should we look for with the Mallows C(p)?