A response Y is a function of three independent variables

Chapter 11, Problem 97SE

(choose chapter or problem)

A response Y is a function of three independent variables $\x_{1}, x_{2}), and \(x_{3}$ that are related as follows:

$Y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+2$

a Fit this model to the n = 7 data points shown in the accompanying table.

b Predict Y when $x_{1}=1, x_{2}=-3, x_{3}=-1$. Compare with the observed response in the original data. Why are these two not equal?

c Do the data present sufficient evidence to indicate that $x_{3}$ contributes information for the

prediction of Y ? (Test the hypothesis $H_{0}: \beta_{3}=0$, using $\alpha=.05$.)

d Find a 95% confidence interval for the expected value of Y, given $x_{1}=1, x_{2}=-3$, and

$x_{3}=-1$.

e Find a 95% prediction interval for Y, given $x_{1}=1, x_{2}=-3, x_{3}=-1$.

Equation transcription:

${x}_{1},{x}_{2}$

${x}_{3}$

$Y={\beta{}}_{0}+{\beta{}}_{1}{x}_{1}+{\beta{}}_{2}{x}_{2}+{\beta{}}_{3}{x}_{3}+\varepsilon{}$

${x}_{1}=1,{x}_{2}=-3,{x}_{3}=-1$

${H}_{0}:{\beta{}}_{3}=0$

$\alpha{}=.05$

${x}_{1}=1,{x}_{2}=-3$

${x}_{3}=-1$

Text transcription:

x{1}, x{2}

X{3}

Y=beta{0}+beta{1} x{1}+beta{2} x{2}+beta{3} x{3}+2

x{1}=1, x{2}=-3, x{3}=-1

H{0}: beta{3}=0

alpha=.05

x{1}=1, x{2}=-3

x{3}=-1

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