If the t ratio for the slope of a simple linear regression equation is equal to 3.614 with a p-value of 0.006, then the slope is

Then the slope is Significantly different from zero at both the 5% level and the 1% level.

Step-by-step explanation:

In statistics for a value to be said to be significant, this value has to be less than p value at the selected level of significance.

Here,

P value = 0.006

5% significance level = 0.05

0.006 < 0.05, so the slope value is significant at 5% significance level.

1% significance =0.001

0.006 is less than 0.01 so the slope coefficient is also significant at 1% significance level

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.