A rocket motor is manufactured by bonding together two types of propellants. The
ID: 3386804 • Letter: A
Question
A rocket motor is manufactured by bonding together two types of propellants. The shear strength of the bond is thought to be related to the age of the propellant when the motor is cast. The Excel file, HW20_ShearStrength.xlsx, contains 20 observations of age and shear strength. We are interested in determining shear strength is linearly related to age of propellant.
Observation Num
Strength (PSI) Y
Age (weeks) X
1
2158.7
15.5
2
1678.15
23.75
3
2316
8
4
2061.3
17
5
2207.5
5
6
1708.3
19
7
1784.7
24
8
2575
2.5
9
2357.9
7.5
10
2277.7
11
11
2165.2
13
12
2399.55
3.75
13
1779.8
25
14
2336.75
9.75
15
1765.3
22
16
2053.5
18
17
2414.4
6
18
2200.5
12.5
19
2654.2
2
20
1753.7
21.5
1. Conduct a hypothesis test to determine if there is a significant linear relationship between age (weeks) and shear strength (psi). Use your scatter plot to determine if your alternative should be testing for a positive or negative relationship. Use a 5% level of significance. (2 points)
2.What is the estimated least squares regression equation? Please write the equation using the values you found for the y-intercept and slope. (2 points)
3.Interpret the slope in the context of this data. (2 points)
4.Interpret the y-intercept in the context of this data if it makes sense to do so. (2 points)
5.What is the value of the correlation coefficient, r? (1 point)
6.What is the value of the coefficient of determination, r2? Interpret the coefficient of determination in the context of this data? (3 points)
7.Find the predicted value for shear strength if age is 21 weeks. (1 point)
8.Paste a scatter plot of the data with the least squares regression line plotted through the points. (2 points)
9.Place a scatter plot of the residuals versus age below. (1 point)
11.To be considered a good fit, a plot of the residuals versus the x variable should be ____________________________________________________. (Complete the statement.) (1 point)
12.In general, why is the method for obtaining the estimated regression equation called the Least Squares Method? (1 point)
Observation Num
Strength (PSI) Y
Age (weeks) X
1
2158.7
15.5
2
1678.15
23.75
3
2316
8
4
2061.3
17
5
2207.5
5
6
1708.3
19
7
1784.7
24
8
2575
2.5
9
2357.9
7.5
10
2277.7
11
11
2165.2
13
12
2399.55
3.75
13
1779.8
25
14
2336.75
9.75
15
1765.3
22
16
2053.5
18
17
2414.4
6
18
2200.5
12.5
19
2654.2
2
20
1753.7
21.5
Explanation / Answer
1.
Using excel we find the all summmary of regression model
The estimated equation is
Y=2625.385-36.9618X
The predict equation is if age is 21 weeks
Y=2625.385-36.9618*21= 1849.188
There is 89% that the data is fitted.
SUMMARY OUTPUT Regression Statistics Multiple R 0.946616 R Square 0.896081 Adjusted R Square 0.890308 Standard Error 99.05156 Observations 20 ANOVA df SS MS F Significance F Regression 1 1522819 1522819 155.2121 2.75E-10 Residual 18 176601.8 9811.212 Total 19 1699421 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 2625.385 45.34684 57.89567 6.58E-22 2530.115 2720.656 X Variable 1 -36.9618 2.966814 -12.4584 2.75E-10 -43.1948 -30.7288Related Questions
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