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A contract engineer studied the rate at which a spilled volatile liquid will spr

ID: 3224448 • Letter: A

Question

A contract engineer studied the rate at which a spilled volatile liquid will spread across a surface. The engineer measured the mass (in pounds) of the spill after a period of time ranging from 0-60 seconds. A quadratic model was fit for the data and the output is below.(10 pts)

Coefficients:

               Estimate Std.        Error             t value          Pr(>|t|)   

(Intercept)     49.3256         1.6820         29.326          < 2e-16 ***

data2$Mass     -16.3007     1.3941        -11.693            2.15e-10 ***

data2$Msquared   1.4153     0.2149      6.587                2.04e-06 ***

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.997 on 20 degrees of freedom

Multiple R-squared: 0.9537,     Adjusted R-squared: 0.9491

F-statistic: 206.1 on 2 and 20 DF, p-value: 4.501e-14

(10 Points)

Write the estimated quadratic model.

Conduct a test of hypothesis to check if the quadratic term is significant.

Is the overall model significant? Conduct a test.

What is the value of the coefficient of determination? Interpret it.

Explanation / Answer

Answer:

A contract engineer studied the rate at which a spilled volatile liquid will spread across a surface. The engineer measured the mass (in pounds) of the spill after a period of time ranging from 0-60 seconds. A quadratic model was fit for the data and the output is below.(10 pts)

Coefficients:

               Estimate Std.        Error             t value          Pr(>|t|)   

(Intercept)     49.3256         1.6820         29.326          < 2e-16 ***

data2$Mass     -16.3007     1.3941        -11.693            2.15e-10 ***

data2$Msquared   1.4153     0.2149      6.587                2.04e-06 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.997 on 20 degrees of freedom

Multiple R-squared: 0.9537,     Adjusted R-squared: 0.9491

F-statistic: 206.1 on 2 and 20 DF, p-value: 4.501e-14

(10 Points)

  

Write the estimated quadratic model.

  Rate of spread = 49.3256-16.3007*mass+1.4153*mass2

Conduct a test of hypothesis to check if the quadratic term is significant.

  Calculated t=6.587, P=0.000 which is < 0.05 level. The quadratic term is significant.

Is the overall model significant? Conduct a test.

Calculated F=206.1, P=0.0000 which is < 0.05 level. The overall model is significant

What is the value of the coefficient of determination? Interpret it.

  coefficient of determination =0.9537

95.37% of variation in rate of spread is explained by the model.

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