Question

8.5 A researcher is interested in determining if an individuals body fat percent- age can be predicted by the amount of weight the individual can bench press. Suppose you have the following data:

BPweight 190, 170, 200, 235, 265, 190, 220, 190

BodyFat 4.6, 5.4, 5.8, 5.9, 6.9, 7.2, 7.4, 7.6

(a) Create a scatterplot to determine if a linear relationship exists between the explanatory variable and the response variable.

(b) Calculate the least squares estimates and write the equation.

(c) Interpret the slope for this equation.

(d) Calculate and interpret the R2 value.

(e) What is the response when the explanatory variable is 177?

(f) Is the independent variable significant and α = 0.05? Why or why not?

(g) Create a 96% confidence interval for the independent variable. (h) Calculate the residual values. (i) Plot the residual values. Is a linear model suggested for this data? Why or why not?

Answer 1

Solution:

Regression Analysis using Excel:-

a.)

b.)

from the above analysis

Regression Equation: y = 0.01x + 4.275

so,Here:

BodyFat=0.01*BPweight + 4.275

c.)

Intercept=4.275

Slope=0.01

d.)R²= 0.081 (from the above analysis)

Here Value is 0.081, which indicates that the relation is very weak.

e.)

explanatory variable is 177

Response:

BodyFat=0.01*BPweight + 4.275

=0.01*177+4.275

=6.045

Solved 5 parts here, for the rest please post again the rest parts.