A researcher plans to study the causal effect of police on crime, using data from a random sample of U. S. counties. He plans to regress the county’s crime rate on the (per capita) size of the county’s police force. (a) Explain why this regression is likely to suffer from omitted variable bias. Which variables would you add to the regression to control for important omitted variables? (b) Use your answer to (a) and the expression for omitted variable bias on slide 5 of the slides on Chapter 6 (it is also Equation (6.1) in SW) to determine whether the regression will likely overor underestimate the effect of police on the crime rate. That is, do you think that βb 1 > β1 or βb 1 < β1 ?

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6