G a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual? A. A residual is a value that is determined exactly, without any error. B. A residual is the amount that one variable changes when the other variable changes by exactly one unit. C. A residual is a value of yminusModifyingAbove y with caret, which is the difference between an observed value of y and a predicted value of y. D. A residual is a point that has a strong effect on the regression equation. b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? The regression line has the property that the ▼ sum of squares sum of the residuals is the ▼ lowest highest possible sum.

for the first question we have the "c” as the correct option

residual is a value of y -y^ which is the difference between an observed value of y and predicted value of y

The residual is a value of y -y ^ which is the difference between an observed value of y and predicted value of y, so answer A is false in The residual mo has errors, option B is false because it is not defined as the quantity that changes a variable and it is false that the residual is a point that has a strong effect on the regression

for question two the correct answer is:

the best fitting straight regression line at the scatter plot points is

b) sum of squares and lowest

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

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐