Question: To study of the relationship between alcohol-insoluble solids (Y) and the tenderometer reading (X), a random sample of 13 sieved-size Alaska peas are analyzed and revealed the following summarized information:

n = 13

\(\sum{X}\) = 4.45 \(\sum{{{X}^{2}}}\) =1.6775

\(\sum{Y}\) = 569 \(\sum{{{Y}^{2}}}\) = 28973

\(\sum{XY}\) =219.4

a) Find the estimate values of intercept, slope, and variance of random error.

b) Find the value of coefficient of determination.

c) Construct a 95% confidence interval for the intercept.

d) Construct a 90% confidence interval for the slope.

e) Construct a 90% confidence interval for the expected value of Y given X = 0.25.

f) Construct a 95% predicted interval for the value of Y given X=0.36.

g) Do you have sufficient evidence to conclude that the intercept is greater than 0?

h) Do you have sufficient evidence to conclude that the slope is less than 135?

i) Do you have sufficient evidence to conclude that the expected value of Y given X= 0.3 is equal to 40?