To determine the future trend of the water levels in the Ogallala Aquifer, we proceed with the given data and perform linear regression analysis. The steps are as follows:
1. Data Analysis:
- Collect the available data points for years and corresponding saturated thickness:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Year} & \text{Saturated Thickness (feet)} \\
\hline
1975 & 107.5 \\
1980 & 95.5 \\
1985 & 84.25 \\
1990 & 73.75 \\
1995 & 63.75 \\
2000 & 55.25 \\
2005 & 47.75 \\
2010 & 40.25 \\
\hline
\end{array}
\][/tex]
2. Linear Regression:
- To model the trend, we fit a linear regression line to the data. The linear regression formula is:
[tex]\[
\text{Thickness} = \text{Slope} \times \text{Year} + \text{Intercept}
\][/tex]
3. Coefficients Determination:
- The linear regression analysis results in the following coefficients:
- Slope: \(-1.920\)
- Intercept: \(3897.074\)
4. Prediction for Future Years:
- To forecast the water levels, we use the regression model to predict the saturated thickness for the year 2020 and 2030.
- Year 2020:
[tex]\[
\text{Thickness}_{2020} = -1.920 \times 2020 + 3897.074 = 18.193 \, \text{feet}
\][/tex]
- Year 2030:
[tex]\[
\text{Thickness}_{2030} = -1.920 \times 2030 + 3897.074 = -1.009 \, \text{feet}
\][/tex]
- Interpretation of Predictions:
- For the year 2020, the predicted saturated thickness is approximately \(18.193\) feet.
- For the year 2030, the predicted saturated thickness is approximately \(-1.009\) feet, which is not feasible because thickness cannot be negative. This indicates that by 2030, the water could deplete entirely based on the current trend.
5. Conclusion:
Given the negative slope and the decreasing values in the predictions, it is clear that the water level in the Ogallala Aquifer is likely to continue to decrease over the next decade, following the historical downward trend. Therefore, the water will continue to decrease.
