Question: This study examines the response of "gas (methane) production" to "storage time (stortime)" . Use the data presented respond to the following questions. Do all calculations by hand or Excel.

data methane

stortime (X) gas (Y)

1 8.2

1 6.6

1 9.8

2 19.7

2 15.7

2 16

3 28.6

3 25

3 31.9

4 30.8

4 37.8

4 40.2

5 40.3

5 42.9

5 32.6

1. Write and completely label the model used to analyze these data.

   	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
   Intercept	1.76	2.512176	0.700587812	0.495909	-3.66723	7.187226
   X	7.993333	0.75745	10.5529572	9.6E-08	6.356963	9.629703

   
   The regression equation is
   \[Gas=1.76+7.993333\,Stortime\]
2. Write the value of the estimate of the parameters.
   \[\begin{aligned} & {{{\hat{\beta }}}_{1}}= \\ & {{{\hat{\beta }}}_{0}}= \\ \end{aligned}\]
3. Calculat e the value of the coefficient determination and comment on it .
4. Predict the gas (methane) production ( \[\hat{y}\] ) when storage time (stortime) is 3.5 .
5. Make an inference about the linear effect of storage time (stortime ) \[{{\hat{\beta }}_{1}}\] . Also, include the appropriate Null and Alternative Hypotheses.
6. Construct a 95 % confidence interval to estimate the parameter \[{{\beta }_{1}}\] . Include a complete inference.

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