Question

1. A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond y is thought to be a linear function of the age of the propellant x when the motor is cast. Twenty observations are shown in the table below. Construct a scatter plot of the data. Determine the relationship between bond strength and age of the propellant, and perform a simple linear regression analysis. Tabulate the following values. a) Marginal change b) coefficient of determination (denoted by R²), and c) Standard error estimate of intercept and slope.

Age (weeks)	Strength
15.50	2158.70
23.75	1678.15
8.00	2316.00
17.00	2061.30
5.00	2207.50
19.00	1708.30
24.00	1784.70
2.50	2575.00
7.50	2357.90
11.00	2277.70
13.00	2165.20
3.75	2399.55
25.00	1779.80
9.75	2336.75
22.00	1765.30
18.00	2053.50
6.00	2414.40
12.50	2200.50
2.00	2654.20
21.50	1753.70

Answer 1

The scatter plot for the above data is as follows

The relationship between bond strength and age of the propellant is

Bond Stenght () = 2625.4 + (-36.962) * xi

The regreesion analysis and output is as follows

Marginal Change

Marginal change is the change in the value of when xi changes by 1

So when xi = 1,

1 = 2625.4 + (-36.962) * 1

When xi = 2

2 = 2625.4 + (-36.962) * 2

The differnce in the two values is -36.962

So the marginal change is -36.962

When it is a linear relationship with one variable, the marginal change will always be the coefficient of x or slope

Coefficient of Determination (R2)

The R-square value from Regression stastistics section of the output attached above is 0.896081

Standard error estimate of intercept and slope

Standard error estimate of intercept from the output attached above is 45.346837

Standard error estimate of slope from the output attached above is 2.966814