Question

NASA is interested in the shear strength of the bond between propellants in a rocket motor and whether it may be related to age of the propellant batch. A random sample of 20 propellant batches is collected and their shear strengths (in pounds per square inch) and ages (in weeks) are recorded. A linear regression model will be used to explore the relationship between the response (shear strength) and the predictor (age of propellant).

1. Write a simple linear regression model (including subscript i) that can be used to analyze the relationship.

2. Explain every term in the model in the words of the problem.

3. State all the model assumptions of the above model.

Answer 1

(1)

A simple linear regression model that can be used to analyze the relationship. between the shear strength of the bond between propellants in a rocket motor and the age of the propellant batch. is written as follows:

,

(2)

Explanation of every term in the model in the words of the problem. :

(i)

(x_i, y_i),   for i = 1,2,...n are the n data pairs:

x_i , for i = 1,2,...n are the independent variable: the age of the propellant batch

y_i, for i = 1,2,...n are the dependent variable: the shear strength of the bond between propellants in a rocket motor

(ii)

is the slope

(iii)

is the y intercept

(iv)

, for i = 1,2,...n is the error term

(3)

All the model assumptions of the above model. are stated as follows:

(i) Linearity: The relationship between x = the age of the propellant batch and y = the bond between propellants in a rocket motor is lenear

(ii) Homoscedasticity: The variance of the residual is the same for any value of x

(iii) Independence: Observations are independent of each other

(iv) Normality: For any fixed value of x, the variable y is normally distributed.