Need Answer for one basic problem on Linear Regression


#1

Assume you have data on weekly prices for 52 weeks for a Shampoo for two competitors A and B. Assume that these prices have been standardized to mean=0 and variance = 1.You want to understand the relationship between the two prices. You decide to perform two regressions. In regression 1, you use price of A as dependent variable, and price of B as independent variable. In regression 2, you use price of B as dependent variable, and price of A as independent variable.

Based on this assumption, which of the following statements is TRUE?

The regression coefficient for the independent variable (Price of B) in regression 1 will be equal to regression coefficient of predictor (Price of A) in regression 2.

The regression coefficient for the independent variable (Price of B) in regression 1 will not be equal to regression coefficient of predictor (Price of A) in regression 2.

Cannot be determined from the information provided


#2

Hi,

This is what I thinkā€¦

Going by the equation of the straight line as y = mx + c, when calculated for x as dependent, this becomes x = (1/m)y - (1/m)c.
For the co-efficients to be equal m = 1/m which will be true when m = 1;
So, if the slope of the line that fits the data is 1, then the co-efficients will be equal and are 1.

Thanks


#3

Just two variables arent you simply finding correlation. The R here should be close or similar to r.


#4

This is what I am doing ,
set.seed(1)
y1 <- rnorm(20,mean=0,sd=1)
y2 <- rnorm(20,mean=0,sd=1)
lm(y1~y2)
lm(y2~y1)

in both cases I have different regression coefficient. Am I not understanding the question properly.
I need Regression Coefficient , not correlation coefficient.