5) the table shows the test scores and the sleep averages of several students. (10 points) test score (%) [88] [75] [76] [92] [96 [94] [83] [90] [99] [65] [77] [88] [82] [83] [94] [97] average sleep (h) [7] [6.5] [6] [7.5] [8] [7] [6.5] [8] [8.5] [5] [7] [9] [8] [8.5] [8.5] [9] points concept addressed 3 correct least squares regression equation 3 explanation of correlation coefficient is correct 4 correct test score is found using regression equation with all work shown a. write the least squares regression equation that models the data. let x = the test score and y = average sleep. b. find the correlation coefficient (r value). explain what this tells you about the association of the data. be sure to describe both the strength and direction in your explanation. c. use the equation to determine the approximate test score of a student who sleeps an average of 8 h a night. show your work.

A) The least squares regression equation has form:

y = m·x + b

In order to calculate slope and intercept, you need to follow these steps (remember x = test scores and y = average sleep, N = total number of students):

1) For each value, calculate x² 

2) For each couple of values, calculate x·y

3) perform the sums: ∑x, ∑y, ∑x² and ∑xy

4) Calculate the slope by the formula:

5) Calculate the intercept by the formula:

6) Assemble the equation.

For steps 1, 2 and 3 values are in the table attached

= 0.091

= -0.343

Therefore the least squares regression equation is:

y = 0.091·x - 0.343

B) Use the inverse of the previously found equation to calculate x (= test score) when y = 8:

x = (8 + 0.343) / 0.091

  = 91.7

Hence, a student who sleeps an average of 8 hours a night scores on average 91.7% on a test.

answer: idk wbu

step-by-step explanation: umm..

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.