The data show the time intervals after an eruption (to the next eruption) of a certain geyser. Find the regression equation,letting the first variable be the independent (x) variable. Find the best predicated time of the interval after an eruption given that the current eruption has a height of 92 feet.Use a significance level of 0.50
To find the regression equation and make a prediction using the given data, you can follow these steps:
1. Start with the given dataset, which should include pairs of observations: the time intervals after an eruption (x-variable) and the corresponding eruption height (y-variable). Let's assume the dataset is provided.
2. Plot the data points on a scatter plot, with the time intervals (x-variable) on the horizontal axis and the eruption heights (y-variable) on the vertical axis.
3. Determine the appropriate regression model. Since you are given a single independent variable (time intervals after an eruption) and one dependent variable (eruption height), a simple linear regression model should suffice.
4. Use statistical software or a calculator to perform the linear regression analysis on the dataset. The regression equation will have the form:
y = b0 + b1 * x,
where y is the predicted eruption height, b0 is the y-intercept, b1 is the slope, and x is the time interval after an eruption.
5. Interpret the regression equation coefficients, b0 and b1, in the context of the problem. The y-intercept (b0) represents the predicted eruption height when the time interval is zero, and the slope (b1) indicates the change in predicted eruption height for each unit increase in time interval.
6. Once you have the regression equation, substitute the given current eruption height (92 feet) into the equation, along with the corresponding time interval. This will give you the predicted time interval after the current eruption.
7. Finally, interpret the prediction by considering the significance level. A significance level of 0.50 typically means that you are 50% confident in your predicted time interval. The higher the confidence level (e.g., 0.95), the more confident you are in the prediction.
Note: Without the given dataset, it is impossible to provide specific numerical values for the regression coefficients or the predicted time interval.