Sometimes, we will get irregular coefficient: consider sell_amount vs sell_price, we should expect a negative coefficient because as the price increases, the selling amount should become less from common sense. But sometimes it may give a positive coefficient.

The possible reason is we put high correlated variables in the predictors: suppose we have both sell_price and product_price in the model, and we know product_price is highly correlated to sell_price. An example is shown below in example 1.

Another possible reason is we recode the missing data: if missing data is at the left, but we recode it to the right(like if x<0 we recode x=99999 which is a very big number).

*Example 1:*

# set up random number seed

set.seed(1000)

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# generate 100 x with x ~ N(5,1)

x=rnorm(100,5,1)

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# Y=5*X

y=5*x+rnorm(100,0,1)

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# X1=100*X

x1=x*100+rnorm(100,0,.2)

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`1)it is reasonable that the regression coefficient is 4.947(while the true value is 5). `

#relation between x and y

lm(y~x)

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`2) because x1=100*x, the coefficient for x1 should be 1/100 of above, as below:`

# relation between x1 and y

lm(y~x1)

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`3) but if we put both x and x1 in the model, then we could not get the positive coefficient for both x and x1. This is because of multicollinearity. `

# put both x and x1 as the predictor

lm(y~x+x1)

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**Example 2:**

`4) another condition is from we recode missing data. Suppose if x<=4 is missing, and we recode missing as 99999.`

# if x<=4, treat it as 99999

x3=ifelse(x>4,x,99999)

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`5) Then the regression coefficient is negative because of the 99999.`

# relation between x3 and y

lm(y~x3)

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The recode issue can be treated as a special case of non-linear relation.

nice blog

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