Week 5 Discussion (4pts) How would you interpret the relaionship between two num

Question

Week 5 Discussion (4pts) How would you interpret the relaionship between two numeric variables when the estimated least squares regression line for them is essentially horizontal (ie. flat)? Please include your name on your posts Week 6 Discussion (4pts) Suppose you want to investigate the relationship between a dependent variable Y and two potential independent variables X1 and X2. Is the R-square value for the equation with both X variables included necessaily at least as large as the R-square value form each equation with only a single X? Explain why or why not Could the R-square for the equation with both X variables included be larger than the sum of the R-square values from the separate equations, each with only a single X included? Please include your name on your posts

Explanation / Answer

5)

If the line is horizontal, Slope = 0

It means, the changes in Y cannot be explained by X

It also means, X and Y are unrelated and their relationship cannot be captured by regression

6)

Scenario-1:

Y =f (X1, X2)

Scenario-2:

Y =f (X1)

R-Square explains how related are X1,X2 with Y

It explains the degree of correlation

As we keep adding more independent variables, R-Square increases

So, Y=f(X1 and X2) will have a higher R-Square than having just Y=f(X1)

It cannot be larger than sum of the R-Square when we have Y=f(X2) and Y=f(X1) because this value could exceed 1

Hope this helps and Please don't forget to rate the answer :)

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