A rocket motor is manufactured by bonding together two types

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

Solution

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	-30.7288