Question

In a study, the protein absorption (Y) for seven concentration levels (X) of that protein were measured: Be Specific with answers

Conc. Level (Xi)	4	6	8	10	12	14	16
Absorption (Yi)	10	15	18	18	24	22	26

a) Find the least squares estimate for the regression line Y_i = b₀ + b₁X_i+ e_i.

b) What would be your estimate of the absorption when the concentration level is 10?

c) Estimate the standard deviation of the error term e_i

d)   Compute the correlation coefficient.

e)   What proportion of the variability in the absorption can be explained using this model   (i.e. what is R²)?

f)    Test the null hypothesis that b₁ = 0 (perform a two-sided test), using α = 0.05. Is the model useful?

g)   Give the p-value to the test in part f ). Verify that the p-value agrees with your conclusion in part f ).

Answer 1

a)

b)

estimate of the absorption when the concentration level is 10=6.857+1.214*10=18.997

c)

d)

correlation coefficient r=

Sxy/(Sxx*Syy)               =

0.9526

e)

proportion of the variability in the absorption can be explained using this model=R² =(0.9526)² =0.9074

f)

as test statsitic is in critical region we reject null hypothesis

wer have sufficient evidence to conclude that model is useful

g)

for 5 degree of freedom and above test statsitic p v alue =0.0009 ; as p value is less than 0.05 level we conclude that model is useful