Check-in #8 - Two-variable Data 1. Manually calculate the residual for each of the following data points using ( 5,2.5) y = 1.1x-3.7 as the line of best fit. Use the formula: R, = y1 7 [a(x,) + b]. Show your work. a) (3.5,-2) b) (5, 2.5) c) Why is the residual in part (a) negative? 2. Mr. Lamont recently opened his pool and is waiting for the water to warm up for swimming. Every 2 days, he measures the temperature of the water. The data is given below. Day 0 2 4 6 8 10 12 Temperature (C) 10.2 11.8 13.2 15.5 17.1 20.4 23.2 a) Using online software (DESMOS or Google Sheets), create a linear regression model. Include a picture of your graph. b) What is the equation of the line of best fit? c) What is the r2 value and what does it mean in the context of the question? 3. If a linear regression has an R-value of r=-0.91, what do you know about the slope of the line? 4. Discuss this image shown in the cartoon. What does the statement "correlation does not imply causation imply in the context of this picture? CORRELATION DOES NOT IMPLY CAUSATION