You work for a regional geological survey and are studying the eruptions of a local geyser. Your study includes modelling the height of the geyser's eruptions based on the period of time since the last eruption. You are going to collect a random sample of 11 of the geyser's eruptions and for each note the time since the last eruption (denoted by x, In hours) and the height of the eruption (denoted by y, In meters). You will also note the product x -y of the time and the height for each eruption. (These products are written in the row labeled "xy"). (a) Click on "Take Sample" to see the results for your random sample. Time since last eruption, x 15 6 11 10 18 11 6 13 20 (in hours) Take Sample Eruption height, y 44.7 17.1 36.8 30.2 42.8 16.7 29.3 21.3 22.4 34.9 43.6 (in meters) XY 670.5 102.6 404.8 302 770.4 83.5 322.3 170.4 134.4 453.7 872 Send data to calculator Based on the data from your sample, enter the indicated values in the column on the left below. Round decimal values to three decimal places. When you are done, select "Compute". (In the table below, > is the sample size and the symbol E xy means the sum of the values xy.) X 5 ? X: 0 Sample correlation coefficient (r): y: 0 Slope (bj ): Exy: 0 y-intercept (bg): Compute(b) Write the equation of the least-squares regression line for your data. Then on the scatter plot for your data, graph this regression equation by plotting two points and then drawing the line through them. Round each coordinate to three decimal places. Regression equation: y = X 5 ? X 2 30- Eruption height (in meters) 20- Time since last eruption (in hours) (c) Use your regression equation to predict the height of an eruption if it has been 12 hours since the last eruption. Round your answer to one decimal place. Predicted height: | meters X 5