STAT 200_ Lab Activity for Sections 2

STAT 200: Lab Activity for Sections 2.6 & 2.7 Activity 1. Butterfly Wings 1 Research Question : Is butterfly growth related to temperature? Body size is known to be related to reproductive success and the ability to move from one habitat to another. A species of butterfly called Boloria chariclea, which is found in Greenland where the climate is changing, was studied for 16 years between 1996-2013. In this study, the scientists measured average wing length in millimeters for each year. They also recorded the average temperature during the larval growth season for the previous summer in degrees Fahrenheit to serve as the predictor. We will focus only on the data from female butterflies, which is found in the dataset Butterfly. Variables of interest : x = average temperature (degrees Fahrenheit) and y = average wing length (millimeters) Understanding the research: 1. What type of study was this based on the summary above? a. Observational study 1. What type of and how many variables are in the research question? a. 2 variables → quantitative Exploratory Data Analysis: 1. Plot your data using a correct plot for the variables of interest. What type of plot did you use? a. Scatter plot Analysis: 1. Is it appropriate to consider the simple linear model for these data? Explain. a. Yes? The data is somewhat linear 1. Write out the regression equation that is provided by Minitab for the simple linear regression model. From the Minitab guide: Fitted Line Plot: Stat -> Regression > Fitted Line Plot -> Enter the response variable under “Response (y)” and the explanatory variable under “Predictor (x)” a. What is the regression equation? Write it below. i. Wing = 23.65 - 0.1344 Temp a. What is the slope? Interpret it in context. i. - 0.1344 a. Does it make sense to interpret the y-intercept? i. ???? 1. Consider the data point for case 3 in the sample. The (x, y) pair = ( 34.5 , 19.5 ). Find this data point on your fitted line plot. Does it appear that the residual for this data point is positive or negative? - 1. Use the regression equation above to calculate the predicted average wing length for this case. Predicted value: 19.01 millimeters 1. Use your previous answers to calculate the residual (error) for case 3. Residual = 13.4708 millimeters. Locate the residual on the fitted line plot