Question

For each exercise, find the equation of the regression line and find the y’ value for the specified x value. Remember that no regression should be done when r is not significant.

27.Class Size and Grades School administrators wondered whether class size and grade achievement (in percent) were related. A random sample of classes revealed the following data.

No. of students	15	10	8	20	18	6
Avg. grade (%)	85	90	82	80	84	92

Find y′ when x = 12.

Answer: R is not significant no regression should be done. Please show work this is a review for an exam coming up. Please do this by hand. Also, specifically show how you find R. Thank you

Answer 1

X	Y	XY	X²	Y²
15	85	1275	225	7225
10	90	900	100	8100
8	82	656	64	6724
20	80	1600	400	6400
18	84	1512	324	7056
6	92	552	36	8464

	X	Y	XY	X²	Y²
total sum	77	513	6495	1149	43969

sample size ,   n =   6      
  
SSxx =    Σx² - (Σx)²/n =   161      
SSxy=   Σxy - (Σx*Σy)/n =   -89      
SSyy =    Σy²-(Σy)²/n =   108      

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.6731
-----------

correlation hypothesis test  
Ho:   ρ = 0
Ha:   ρ ╪ 0

t-test statistic = r*√(n-2)/√(1-r²) = -0.6731*√4/√(1-(-0.6731)²) = -1.820  

DF=n-2 =   4, α=0.05
critical t-value = ±2.7764 [from t table]

since, test stat = -1.820> critical value = -2.7764, null hypothesis is not rejected

so, correlation coefficient is not significant

: R is not significant no regression should be done