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

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

b) Write the value of the estimate of the parameters.

\[\begin{aligned} & {{{\hat{\beta }}}_{1}}= \\ & {{{\hat{\beta }}}_{0}}= \\ \end{aligned}\]

c) Calculate the value of the coefficient determination and comment on it.

d) Predict the gas (methane) production ( \[\hat{y}\] ) when storage time (stortime) is 3.5 .

e) Make an inference about the linear effect of storage time (stortime) \[{{\hat{\beta }}_{1}}\]. Also, include the appropriate Null and Alternative Hypotheses.

f) Construct a 95 % confidence interval to estimate the parameter \[{{\beta }_{1}}\]. Include a complete inference.