Question

This is like my 3rd time re asking this question because later I figured out 2 typos which is the P-value is 0.0000 and i can't get it to space where you see it off from the left of the anova table, and I missed putting a minus sign on part f. So thats why you keep seeing a duplicate questions from me.

1. A scientist study the relation of x=salinity level and y=nitrate level. He fitted a simple linear

regression of y on x and got the following ANOVA table.

Analysis of Variance Table

Source                         df                    SS                    MS                  F                      p-value

X                                 1                      64.496             64.496 0.0000

Residual                      6                      6.113

a. MSE and F-statistic are missing in the table, please fill in.

b. What is his sample size n?

c. What is y’s total variation?

d. what is the sample standard deviation s_y?

e. If we know x and y are negatively correlated, what is the sample correlation coefficient

between x and y?

f. If we know the fitted regression line is y = 326.976 - 8.404x, what is x’s sample standard deviation s_x?

Answer 1

Source	df	SS	MS	F	p vlaue
regression	1	64.496	64.496	63.30	0.0002
error	6	6.113	1.019
total	7	70.609

a)

MSE =6.113/6 =1.0188

F +MS(X)/MSE =63.3038

b)

n =total(dF)+1 =8

c)  y’s total variation =70.609

d)  sample standard deviation s_y =sqrt(SST/(n-1))=sqrt(70.609/7)=3.176

e) sample corelation coeffiicent =-sqrt(SSR/SST) =-sqrt(64.496/70.609)= -0.9557

f)

x’s sample standard deviation s_x =r*Sy/b1= -0.9557*(3.176)/(-8.404)= 0.3612