Question

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Feeding behavior of black bream fish. In Brain and Behavior Evolution (April 2000), Zoologists conducted a study of the feeding behavior of black bream fish. The zoologists recorded the number of aggressive strikes of two black bream fish feeding at the bottom of an aquarium in the 10-minute period following the addition of food. The next table lists the weekly number of strikes and age of the fish (in days).

Week ? ? ? ? ? ? ? ? ?

Number of Strikes ?? ?? ?? ?? ?? ?? ?? ?? ??

Age of Fish (days) ??? ??? ??? ??? ??? ??? ??? ??? ???

We want to fit a straight-line model relating number of strikes(y) to age of fish (x).

a. Find ???? , ???? ??? ???? .

b. Find the least squares estimators ?̂ 0 and ?̂ 1 and give the least squares prediction equation.

c. Give a practical interpretation of the value of ?̂ 1.

d. Find ? 2 , the estimator of the variance ? 2 of the random error term ?.

e. Use the least squares model to estimate the mean number of strikes if the age of fish is 170 days.

f. List the assumptions required for the regression analysis.

g. Is there evidence that age of fish contributes information for the prediction of number of strikes? Conduct a hypothesis test using ? = 0.1.

h. Find a 97 % Confidence interval for ?1.

Answer 1

AS given above here Y denotes the number of strikes

and X denotes the age of fish.

So we will fit linear regression model on the given data as follows:

Regression equation of y on x is given by:

Where:

and

A)

Then from the above formulas and calculations:

B)

From the above given equation of regression it is given by:

C)

Practical interpretation of is that if we increase the age of fish by one day then on an average number of strikes will decrease by 0.8195 units.

D)

Here estimate of S2 is given by MSE (Mean square error)

= 238.24

E)

put x = 170 in the regression equation .