Warm Up A method to estimate the age of a lobster was investigated in a 2007 study. The length of the exterior shell (in mm) was compared to the known age of 10 lobsters. The data is below. Lobster Length Age Lobster Length Age 1 63.32 1.0 6 79.32 1.42 2 110.64 2.18 7 133.95 2.50 3 105.07 1.82 8 145.78 3.42 4 152.04 4.08 9 118.99 2.17 5 152.73 3.41 10 123.51 2.50 1) Find the equation of the LSRL and the value of r. 2) What is the meaning of the slope and y-intercept in the context of the problem.
Computer Output Data is often presented in a summary form of a computer program output. For the warm up problem we might get the following: ------------------------------------------------------------------- Dependent variable is: Age R squared = 90.286% S = 0.316 Variable Coefficient SE(Coeff) t-ratio p-value Constant -1.13552 0.4436 -2.56 0.0158 Shell Length 0.030249 0.0035 8.62 <0.0001 -------------------------------------------------------------------- What is the LSRL and r? What is the predicted age of a lobster with a shell length of 100 mm?
Practice Assembly line workers were studied to find a correlation between experience (in months) of the worker and the time (in minutes) to complete an assembly task. The data is summarized below. Dependent variable is: Assembly time R squared = 62.0% S = 9.790 Variable Coefficient SE(Coeff) t-ratio p-value Constant 84.683 5.602 15.12 0.000 Experience -0.30411 0.04963 -6.13 0.000 -------------------------------------------------------------------- 1) What is the LSRL and r? 2) What is the predicted assembly time for a worker with 120 months of experience?
Residual Plots Residuals appear random with no pattern. Residuals have clear non-linear pattern.
Practice A method to estimate the age of a lobster was investigated in a 2007 study. The length of the exterior shell (in mm) was compared to the known age of 10 lobsters. The data is below. Lobster Length Age Lobster Length Age 1 63.32 1.0 6 79.32 1.42 2 110.64 2.18 7 133.95 2.50 3 105.07 1.82 8 145.78 3.42 4 152.04 4.08 9 118.99 2.17 5 152.73 3.41 10 123.51 2.50 1) Make a residual plot of the data. 2) Is it reasonable to assume a linear relationship between lobster length and age?
Activity – Launching Marbles - What is the correlation between the angle of the launch ramp and the distance a marble travels? - Work with your table to measure the distance a marble will roll when launched down a ramp propped against an increasing number of Stats books. - Launch your marble using stacks of 1 to 6 books (6 data points). Measure the distance in inches. - Write your data as an ordered pair on the board (# of books, distance in inches)
Activity – Launching Marbles 1) Enter the number of books in L1 and the distance in L2. 2) Make a scatterplot and comment on it (don’t need to copy it) 3) Calculate the correlation coefficient r and the LSRL. 4) Make a plot of the residuals. 5) Do you think a linear model is suitable for the correlation between number of books and distance? Why or why not? 6) Using the LSRL estimate the distance a marble would roll with 7 books. Do you think this is a good estimate? Why or why not?
Chapter 3 Review A psychological study in 2010 asked 62 volunteers to rate the trustworthiness of a man based on a picture of his face. Researchers also measured the width-to-height ratio for each pictured face. The percent who chose the face as trustworthy vs. the width-to-height ratio are shown: W-H Ratio Trust W-H Ratio Trust W-H Ratio Trust 1.75 58 1.90 30 1.95 65 2.00 28 2.05 8 2.05 58 2.10 35 2.10 50 2.10 62 2.15 15 2.20 22 2.25 20 2.30 8 2.40 35 2.70 11 1) Make a scatterplot and interpret the plot. 2) Find the equation of the LSRL and the correlation coefficient r. 3) What is the value of r2 and what is its meaning in context? 4) Is a linear model appropriate for this data? Why or why not?