A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table. Test Scores
Student First Test Grade Second Test Grade
1 42 81
2 51 74
3 88 62
4 99 57
5 54 72
6 66 73
7 87 63
8 99 57
9 97 58
10 89 63
11 42 77
12 71 63
13 96 55
14 56 76
15 75 69
16 57 70
17 62 75
18 89 63
19 50 72
20 56 72
21 89 57

Step 1 of 2 : Using statistical software, estimate the parameters of the model

Second Test Grade=β0+β1(First Test Grade)+εi.

Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.

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

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x