Show all work and use correct notation unless otherwise stated! I expect all formulas to be stated. When needed, you may round final answers to at least two decimal places. You only need to check conditions when doing a complete CI or test, or if specifically asked. Do the CI or test even if you feel the conditions are not met - just state your reservations. When SPSS output is given, it must be used when possible, to answer the question to receive full credit (numbers must be stated directly from the output) 1. (10 points) There is a geyser at Calistoga, in California's Napa Valley, that is considered to be another "Old Faithful" geyser. We want to use the time between eruptions (time) of this geyser to predict the length of the eruption (length). Time and length, both given in minutes, are recorded for 9 randomly selected eruptions. The data was entered into SPSS and the following output obtained: Unstandardized Standardized Coefficients Coefficients Model Std. Error Beta Sig. (Constant) -.378 .376 -1.005 .348 time . 185 032 911 5.842 .001 We want to test if when the time between eruptions increases the length of the eruption also tends to increase using the SPSS output above. Answer the following questions about this test. a) (4 pts) State the regression line for this problem using correct notation. b) (4 pts) Give a good interpretation of the slope in the context of this problem. c) (2 pts) What will be the sign of the correlation coefficient for this