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 ***
---
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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