Frap Time! Linear Regression

You will have a question to try to answer and I’ll give you 15 minutes. Then we will stop, look at some commentary then grade each others’. You won’t have one for homework. Instead you are to read the summaries and start studying Ch 3 (Linear Regression). Also start reading the summaries in Ch 4 (Designing Studies). That is what your second free response will be about.

In this question you were presented with data, a scatter plot, a residual plot, and computer output of the data. Part a’s intent was to see if you could combine all that data to assess linearity. Most importantly you must have discussed the residual plot and not discuss the r and r-squared values. Part b’s intent was to see if you were able to determine what the interpretation of slope would look like without calling it slope. Part c was straight forward, you need to know how to interpret r-squared in context. Part d wanted you to understand the concept of extrapolation.

Solutions Part A: Yes, a linear model is appropriate. The scatterplot shows a strong, positive linear association between the number of railcars and fuel consumption. The residual plot shows a random scatter of points above and below zero.

Solutions Part B: According to the computer output, fuel consumption will increase by 2.15 units for each additional railcar. Since the fuel consumption is $25 per unit, the average cost of fuel per mile will increase by 25 x 2.15 = $53.75 for each additional railcar.

Solutions Part C: The regression output indicates r- squared = 96.7% (or 0.967). Thus, 96.7% of the variation in fuel consumption is explained by using the linear regression model with the number of railcars as the explanatory variable.

Solutions Part D: No, the data set does not contain any information about fuel consumption for any trains above 50 railcars. Using the regression model to predict the fuel consumption for 65 railcars is known as extrapolation, and this is not reasonable.

Scoring

Example to grade together

No you get to trade with someone and write and E, P, or I next to each part and give them an overall score. When finished trade back and discuss your grading with each other. BE PICKY - you are LEARNING, not getting graded!