The data show the time intervals is after

an eruption(to the next eruption) of a certain geyser. Find the regression equation, letting the first variable be the independent (r) variable. Find the best predicted time of the interval after an eruption that the current eruption has a height of 149 feet. Use a significance
level of 0.05 Height(ft) interval after(min) What is the regression equation. round to two decimal places
as needed.

Height(ft) 108 124 108 152 109 138 137 103

interval after (min) 77 73 81 87 69 91 90 68

If you need to show the work by hand, you can develop the regression equation in the following format:

predicted y = a + bx
...where a represents the y-intercept and b the slope.

Note: x = height; y = time

To get to that point, here are some formulas to calculate along the way.

To find a:
a = (Ey/n) - b(Ex/n)

Note: E means to add up or to find the total.

To find b:
b = SSxy/SSxx

To find SSxy:
SSxy = Exy - [(Ex)(Ey)]/n

To find SSxx:
SSxx = Ex^2 - [(Ex)(Ex)]/n

Once you have the formula, you can determine the best predicted time using 149 for feet.

I hope this will help get you started.

sfds

To find the regression equation, we will use a statistical software or calculator. However, I can guide you through the steps to calculate it manually. Here's how:

Step 1: Create a scatter plot
Plot the data points on a scatter plot with the "height" on the y-axis and "interval after" on the x-axis.

Step 2: Calculate the mean of both variables
Find the mean of the "height" variable and the mean of the "interval after" variable. Let's denote them as ȳ (mean of height) and x̄ (mean of interval after).

Step 3: Calculate the deviations from the mean
For each data point, calculate the deviation from the mean for both variables. Denote the deviation from the mean of "height" as y and from the mean of "interval after" as x.

Step 4: Calculate the sums of products and squares
Calculate the sum of the products of the deviations from the mean for each data point (x - x̄)(y - ȳ), as well as the sum of the squared deviations from the mean for "interval after" (∑(x - x̄)^2).

Step 5: Calculate the regression coefficients
The regression equation Y = a + bX can be calculated as:

b = (∑(x - x̄)(y - ȳ)) / (∑(x - x̄)^2)
a = ȳ - b * x̄

b represents the slope of the regression line, and a represents the y-intercept.

Step 6: Substitute the values into the regression equation
Substitute the calculated slope and y-intercept into the regression equation to obtain the final equation.

Once you have the regression equation, you can use it to predict the time interval after an eruption for a given height.

Please note that due to the complexity of this calculation, it is recommended to use statistical software or a calculator with regression capabilities to obtain precise results.