Question

1. In studying seafood consumption and Omega-3 levels the following data was gathered Seafood Omega-3 Consumption Levels (grams/day) (nmol/l) 12 96 110 138 175 205 210 325 1.54 1.35 1.76 2.45 3.56 4.11 4.03 a) Find the correlation coefficient, r. b) Find the coefficient of determination, CD. What does this tell us? c) Find the best fitting linear relationship between the consumption of seafood and the Omega-3 levels. d) Why do we need to calculater as well as a best fit line in determining if a linear relationship exists? e) Use the linear relationship to find the predicted Omega-3 levels along with the associated 90% confidence/prediction interval for the Omega-3 level given a daily seafood consumption of 310 gm/day. 1) Should we use this relationship to predict the Omega-3 level of someone who consumes 500 grams/day of seafood daily? Why or why not?

Answer 1

SOLUTION- WE USE MINITAB 16 TO SOLVE THE GIVEN PROBLEM

A.) WE COMPUTE THE CORRELATION COEFFICIENT AS:

ENTER THE VALUES IN TWO DIFFERENT COLUMNS>STAT>BASIC STATISTICS>CORRELATION>ENTER THE VARIABLES>Ok

The correlation coefficient(r) is 0.899.

B.) THE COEFFICIENT OF DETERMINATION(C.D) IS BASICALLY $r^{2}$

HENCE , CD=0.808. THE VALUE INDICATES A STRONG RELATIONSHIP AMONG BOTH THE VARIABLES.

C.) STEPS: STAT>REGRESSION>REGRESSION>ENTER OMEGA LEVEL AS THE RESPONSE AND SEAFOOD CONSUMPTION AS PREDICTOR>OK

THE LINEAR FITTED REGRESSION EQUATION OBTAINED IS

OMEGA_LEVEL= 0.259 + 0.0135*SEAFOOD CONSUMPTION.

D.) BY THE VALUE OF CORRELATION COEFFICIENT, WE GET TO KNOW IF A RELATIONSHIP EXISTS AMONG THE VARIABLES. BUT BY FITTING A LINE, WE MAY ESTABLISH THE FACT THAT THERE EXISTS A LINEAR RELATION IF THE LINE OBTAINED IS OF THE FORM Y=M*X+C

E.)