The following data were collected in an experiment to study the relationship between

Chapter 8, Problem 15

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The following data were collected in an experiment to study the relationship between extrusion pressure (in KPa) and wear (in mg).

$x$	150	175	200	225	250	275
$y$	$10.4$	$12.4$	$14.9$	$15.0$	$13.9$	$11.9$

The least-squares quadratic model is $y=-32.445714+0.43154286 x-0.000982857 x^{2}$.

a. Using this equation, compute the residuals.

b. Compute the error sum of squares SSE and the total sum of squares SST.

c. Compute the error variance estimate $s^2$.

d. Compute the coefficient of determination $R^2$.

e. Compute the value of the $F$ statistic for the hypothesis $H_{0}: \beta_{1}=\beta_{2}=0$. How many degrees of freedom does this statistic have?

f. Can the hypothesis $H_{0}: \beta_{1}=\beta_{2}=0$ be rejected at the $5\%$ level? Explain.

Equation Transcription:

$y=-32.445714+0.43154286x-0.000982857{x}^{2}$

$SSE$

$SST$

${s}^{2}$

${R}^{2}$

${H}_{0}:{\beta{}}_{1}={\beta{}}_{2}=0$

Text Transcription:

y=-32.445714+0.43154286x-0.000982857x^2

SSE

SST

s^2

R^2

H_0:beta_1=beta_2=0

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