A rocket motor ls manufactured by bonding together two types of propellants, an
ID: 3375481 • Letter: A
Question
A rocket motor ls manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond is thought to be a linear function of the age of the propellant when the motor is cast. Shear strength and age of a random sample of motors was collected (a) The following figure shows the scatterplot of these data. Discuss if the simple linear Signif. codes:00.0010.01 0.00.11 Residual standard eror: 99.05 on 18 degrees of freedom Multiple R-squared: 0.8961, F-statistic: 155.2 on 1 and 18 DF, p-value: 2.753e-10 Adjusted R-squared: 0.8903 regression model is appropriate for the relationship between these two variables based on the plot. bl Compute the correlation coefficient between shear strength and age of these motors based on the R output. (c) Based on the above output, report the estimated (fitted) regression equation for the relationship between shear strength and age of these motors. Age (wed [d Interpret the slope of the fitted line in terms of shear strength and age of motors. The following output was obtained from the summary function and Im function in R. Call: lnifor mula-?" ?) Residuals: e If it makes sense, interpret the y-intercept. Otherwise, clearly explain why y-intercept does not make sense. Min 1Q Median 3Q Max 233.08-52.54 28.73 66.13 106.22 Coefficients: (Intercept) 2625.385 45.347 57.902e-16 (f) Estimate the mean shear strength of a motor made from propellant that is 10 weeks old. Estimate Std. Error t value PrlItI) -36.962 .967-12.46 2.75e-10* g) Estimate the mean shear strength of a motor made from propellant that is 30 weeks old.Explanation / Answer
b)
correlation coefficient = R Square ½ = 0.89611/2 = - 0.946626
Note: Negative sign is concluded from the scatter plot.
c)
Regression Equation:
Shear Strength = 2625.385 – 36.962 * Age
d)
Interpretation of Slope:
The amount by which the response variable(Shear Strength) increases or decreases, on average, when the explanatory variable(Age) increases by one units.
e)
The y intercept is the value at which the fitted line crosses the y-axis. In this case, its value is 2625.385.
In this case, y intercept does not make sense as when Age is Zero, the Shear Strength would be 2625.385 which is absurd as Age can never be zero.
f)
When Age = 10,
Shear Strength = 2625.385 – 36.962 * 10 = 2255.765 units
g)
When Age = 30,
Shear Strength = 2625.385 – 36.962 * 30 = 1516.525 units
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