In an experiment to model the shear strength (Y, in psi) of the binding of two p

Question

In an experiment to model the shear strength (Y, in psi) of the binding of two propellants in a rocket motor, as a function of the age (X) of the propellant (in week), 25 observations of strength and age were collected.   The greatest value of age in the sample was 216 weeks. The following data were obtained:

DATA

xy = 65164.04

x = 778.7

y= 2050

x2 = 26591.6

y2 = 172891.5

n=25

a. Determine the predictive equation for the simple linear regression model, using the sums above. Show   

b. Perform a hypothesis test to determine if the equation is useful for prediction (or if the regression slope was significant).  

c. Use the equation to predict shear strength when age =200 weeks.

d. Determine the 99% Confidence Interval for the predicted strength (at 200 weeks).   (Use the S values above to help calculate Sxx, Syy, or SSE (if necessary) from the formulas in the formula sheet. Do not try to predict each y value and each error, and then sum the error squares – it is unnecessary.)
e.      A student performs a regression analysis of height (Y) versus age (X) and determines that the R-square value was 0.65. Write a statement interpreting this R-square value.

Explanation / Answer

Ans:

Regression eqn:

y=a+bx

slope, b=(25*65164.04-778.7*2050)/(25*26591.6-778.7^2)=0.561

y-intercept,a=(2050-0.561*778.7)/25=64.526

y=64.526+0.561x

c)when x=200

y=64.526+0.561*200=176.73

e)R2=0.65

it means cofficient of determination is 0.65,which indicates the 65% of the linear variation of dependent variable y is explained by the independent varaible x.

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