1.  The equation used to calculate Cab Fare is y = 0.75x + 2.5 where y is the cost and x is the number of miles traveled. 1. What is the slope in this equation? What does it represent in this context? 2. What is the y-intercept in this equation? What does it represent in this context? 3. What is the cost for a cab ride where you travel 3.5 miles? 4. If your cab ride costs $17.30, how far did you travel?

2. Slide 8 - 2  The following is a scatterplot of total fat versus protein for 30 items on the Burger King menu:

3. Slide 8 - 3  The correlation in this example is 0.83. It says “There seems to be a linear association between these two variables,” but it doesn’t tell what that association is.  We can say more about the linear relationship between two quantitative variables with a model.  A model simplifies reality to help us understand underlying patterns and relationships.

4. Slide 8 - 4  The linear model is just an equation of a straight line through the data. o The points in the scatterplot don’t all line up, but a straight line can summarize the general pattern with only a couple of parameters. o The linear model can help us understand how the values are associated.

5. Slide 8 - 5  The model won’t be perfect, regardless of the line we draw.  Some points will be above the line and some will be below.  The estimate made from a model is the predicted value (denoted as ).

6. Slide 8 - 6  The difference between the observed value and its associated predicted value is called the residual.  To find the residuals, we always subtract the predicted value from the observed one:

7. Slide 8 - 7  A negative residual means the predicted value’s too big (an overestimate).  A positive residual means the predicted value’s too small (an underestimate).  In the figure, the estimated fat of the BK Broiler chicken sandwich is 36 g, while the true value of fat is 25 g, so the residual is –11 g of fat.

8. From the Carnegie Foundation math.mtsac.edu/statway/lesson_3.3.1_version1.5A

9. Determines the effectiveness of the regression model

10. Observed y - predicted y

11. Total Time (minutes) Total Distance (miles Predicted Total Distance Residuals (observed – predicted) 325154.4-3.4 193031.9 2847 3656 1727 2335 4165 2241 3773 2854

12. Total Time (minutes) Total Distance (miles Predicted Total Distance Residuals (observed – predicted) 325154.4-3.4 193031.9 -1.9 2847 47.5-0.5 3656 61.3-5.3 1727 28.5-1.5 2335 38.8-3.8 4165 70.0-5 2241 37.13.9 3773 63.19.9 2854 47.56.5

13.  A scatterplot of Residuals vs. X

15.  If it the model is appropriate, then the plot will have a random scatter.  If another model is necessary, the plot will have a pattern. Pattern = Problem

18. Determine, just by visual inspection, if the linear model is appropriate or inappropriate.

20. 1. Does their appear to be a pattern in the residual plot? Yes, quadratic. 2. Does this support your original guess? You must now see that a linear model does NOT fit this data.

22. 1. Does their appear to be a pattern in the residual plot? Yes, it fans out as x increases. 2. Does this support your original guess? You must now see that a linear model does NOT fit this data.

24. 1. Does their appear to be a pattern in the residual plot? Yes, it looks quadratic. 2. Does this support your original guess? This was very tricky. The scale was very small. You must now see that a linear model does NOT fit this data.

26. 1. Does their appear to be a pattern in the residual plot? Yes, it seems decrease as x increases. 2. Does this support your original guess? This was tricky. You must now see that a linear model does NOT fit this data.

27. Calculating Airfare

28. Worksheet