Exodus 13

According to the Law of the Firstborn, what shall you do to the firstborn of a donkey, if you will not redeem it?break its neck. Ex. 13:13Why did the Lord not lead the children of Israel out of Egypt by the way of the land of the Philistines?Lest the people change their minds when they see war and return to Egypt. Ex. 13:17God led the children of Israel of out Egypt by which way?The wilderness of the Red Sea. Ex. 13:18When God led the people around by way of the wilderness of the Red Sea, the children of Israel went up which way out of the land of Egypt?In orderly ranks. Ex. 13:18Whose bones did Moses take with him when he left Egypt?bones of Joseph. Ex. 13:19The children of Israel took their journey from Succoth and camped where?In Etham at the edge of the wilderness. Ex. 13:20When the children of Israel took their journey from Succoth, the Lord went before them by day to lead the way in what?in a pillar of cloud. Ex. 13:21When the children of Israel took their journey from Succoth, the Lord went before them by night to lead the way in what?in a pillar of fire. Ex. 13:21

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Using the appropriate output for each case study, do the following parts, and, if you have studied the optional $F$ test, also do the other given parts.

The Excel and Minitab outputs of a simple linear regression analysis of the data set for this case are given in Figures $13.12$ and $13.13$ . Recall that labeled Excel and Minitab outputs are shown on the figure on the said page.

a Find the least squares point estimates $b_o$ and $b_1$ of $\beta_0$ and $\beta_1$ on the output and report their values.

Figure $13.12$ Excel Output of a Simple Linear Regression Analysis of the Natural Gas Consumption Data

\begin{array}{lrrrrr} \text{Regression Statistics}\\ &&\\ \text{Multiple R} & 0.9484\\ \text{R Square} & 0.8995\\ \text{Adjusted R Square} & 0.8827\\ \text{Standard Error} & 0.6542\\ \text{Observations} & 8\\ &&\\ \text{ANOVA} & \text{df} & \text{SS} & \text{MS} & \text{F} & \text{Significance F}\\ \text{Regression} & 1 & 22.9808 & 22.9808 & 53.6949 & 0.0003\\ \text{Residual} & 6 & 2.5679 & 0.4280\\ \text{Total} & 7 & 25.5488\\ &&\\ & \text{Coefficients} & \text{Standard Error} & \text{t Stat} & \text{P-value} & \text{Lower 95\\\%}\\ \text{Intercept} & 15.8379 & 0.8018 & 19.7535 & 1.09\text{E-}06 & 13.8760\\ \text{TEMP} & -0.1279 & 0.0175 & -7.3277 & 0.0003 & -0.1706 \end{array}

Figure $13.13$ Minitab Output of a Simple Linear Regression Analysis of the Natural Gas Consumption Data

\begin{array}{lrrrrr} \text{Analysis of Variance}\\ \text{Source} & \text{DF} & \text{Adj MS} & \text{Adj MS} & \text{F-Value} & \text{P-Value}\\ \text{Regression} & 1 & 22.9808 & 22.9808 & 53.69 & 0.000\\ \text{ Temp} & 1 & 22.9808 & 22.9808 & 53.69 & 0.000\\ \text{Error} & 6 & 2.5679 & 0.4280\\ \text{ Lack-of-Fit} & 5 & 2.3229 & 0.4646 & 1.90 & 0.500\\ \text{ Pure Error} & 1 & 0.2450 & 0.2450\\ \text{Total} & 7 & 25.5488\\ &&\\ \text{Model Summary}\\ \text{S} & \text{R-sq} & \text{R-sq(adj)} & \text{R-sq(pred)}\\ 0.6542089 & 89.95\% & 88.27\% & 81.98\%\\ &&\\ \text{Coefficients}\\ \text{Term} & \text{Coef} &\text{SE Coef} & \text{T-Value} & \text{P-Value} & \text{VIF}\\ \text{Constant} & 15.838 & 0.802 & 19.75 & 0.000\\ \text{Temp} & -0.1279 & 0.0175 & -7.33 & 0.000 & 1.00\\ &&\\ \text{Regression Equation}\\ &&\\ \text{GasCons}=15.838-0.1279\ \text{Temp}\\ &&\\ \text{Variable} & \text{Setting} & \text{Fit} & \text{SE Fit} & \text{95\\\% CI} & \text{95\\\% PI}\\ \text{Temp} & 40 & 10.7210 & 0.241483 & (10.1301, 11.3119) & (9.01462, 12.4274) \end{array}

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