2. A contract engineer studied the rate at which z spilled volatile liquid will
ID: 3224445 • Letter: 2
Question
2. A contract engineer studied the rate at which z spilled volatile liquid will sprcad across a Nurface. The engineer measured the maNN (in paunde) of the spill after a Period of time ranging from D-60 seconds. A quadratic model was fit for the data and the output is below 10 poe) Estimate Std. Error t value (Intercept) 49.3256 1.6520 21.326. 2e-16 2.15e-10 data 25Mass 163007 1.394l 11 E13 data25Msquared 1.4153 0.2149 6.587 Siapit 0 0.001 0.01 0.05 0.1 Residual standard error: 3.997 20 degrees of freedom Multiple R-squared: 0s537 Adjusted R -squared 0.0491 F-statistic: 206.1 on 2 and 20 DF Revalec: 4.50le-14 (10 Points a) Write the estimated quadratic model Conduct test of hypothesis check if the quadratic term is significant. e) the overall model significant? Conduct a test. dh What is the value of the coefficient of determination? Interpret it.Explanation / Answer
a. Here Intercept = 49.3256, Data25Mass Coefficient = -16.3007, Data25MassSquared coefficient = 1.4153
Say, Y = rate of spread, X = Mass of the spill.
Hence, from the given output, the estimated quadratic model would be:
Y = 49.3256 -16.3007X + 1.4153x2 ------------------------------------------- (1)
b. Here H0: Y with variation of Xi = Y without variation of Xi
H1: Y with variation of Xi != Y without variation of Xi
Since, Pr(|>t|) << 0.05 for Intercept and oth the Coeffs, we can reject the hypothesis that Y remains uneffected with variation of X's (here X0 = Intercept, X1 = Data25Mass and X2 = Data25MassSquared).
Which means that individual terms (Intercept, Mass and Square of Mass) at eqn (1) significantly effect the outcome, Y = rate of spread.
c. From the F-Test result of the overall model, p =1.501e-14 << 0.05.
That provides evidence that overall model is significant.
d. Coefficient of determination multiple R-Squared = 0.9537 implies that 95.37% of the variation of the output is explained by the variation of mass and square of mass.
Also, Adjusted R-squared = 0.9493 implies that 94.93% of variation at outcome is explained by variation of the variables adjusted to combination of their significance to the outcome variation.
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