Tonight STUDY, STUDY, STUDY, STUDY, STUDY!

• Look over the topics listed below for tomorrow's test
• Complete the review packet provided in class on Monday (and check your answers below)
• Look over your notes--maybe even type up an outline of your notes to help remember key concepts, definitions, formulas, interpretations
• Do the extra practice problems at the bottom of this post
• Look over your past quizzes and classwork assignments

Thursday's Test (11/15) = AP MC and AP FR!

• Concepts to know:
• How to read a computer output (write LSRL)
• Find correlation given a computer output
• How to find the LSRL, r, and R^2 with your graphing calculator
• View a scatterplot and a residual plot on your graphing calculator
• Describe an association
• Determine if a linear model is appropriate
• Interpret slope
• Interpret y-intercept
• Interpret R^2
• Use an equation to make predictions
• Calculate the residual for a prediction
• Use residuals and the equation to find an actual value
• Interpret the meaning of a residual
• Describe how a point may influence slope, intercept, and/or correlation and explain why
• Use a re-expressed model to make predictions
• Determine if a prediction would be too large, too small, or accurate given a residual plot

Here are the answers to the review packet provided in class Monday:

• Front page:
• 4.) A response variable.... C
• 3.) It's easy to measure... A
• The model sqrt(distance)... A
• For the model y = 1.9... E
• Page 2:
• 13a.) r = -0.9529 (always check slope to see if the correlation is + or -)
• 13b.) 40.3266 - 5.95956(4) = 16.48836 units/cc
• 13c.) The estimate is likely to be too high because, based on the residual plot, the residuals around a predicted value of 16.5 are negative, so I would expect the residual for this prediction to be negative which means our prediction is an overestimate (too large).
• 13d.) This model is better than the original because for this (re-expressed) model the residual plot does not have a clear pattern (but for the original model there was a clear curve in the residual plot).
• 13e). Log(cnn) = 1.80184 - 0.172672(4); concentration = 12.9167 units/cc
• Page 3:
• E
• We know the second model/Regression II is a better fit because Regression I showed a clear curve in the residual plot, while the residual plot for Regression II is more scattered.
• We can then narrow this down to B or E; we know there is a nonlinear relationship between x and y, because the model of "x vs. y" was Regression I, and the residual plot for Regression I showed that the relationship was not linear (a linear model was not appropriate).
• Page 4:
• 1.) The association between John's walking speed and pulse rate is strong, roughly linear, and positive, with r = 0.9935. In the scatterplot, the higher John's walking speed the higher is pulse rate.
• 2.) A linear model does appear to be appropriate for the relationship between John's walking speed and pulse rate because both variables (walking speed and pulse rate) are quantitative and the scatterplot is roughly linear. (We would also like to check to see if a residual plot does not have a pattern--tomorrow a residual plot will be provided on the test.)
• 3.) predicted pulse rate = 63.457 + 16.2809(walking speed)
• 4.) 63.457 + 16.2809(4.5) = 136.72105 bpm
• 5.) Residual = actual - predicted = 141 - 136.72105 = 4.27895 bmp
• Note: actual value was estimated from the scatterplot
• 6.) Point would either be at the "bottom right" of the graph or the "top left" of the graph. (Feel free to send a picture via Remind if you want me to take a look). 
• 7.) The point should be "at the middle of the see-saw" so it has no leverage and should be above/away from or below/away from the pattern/trend.(Feel free to send a picture via Remind if you want me to take a look). 
• 8.) This point should follow the trend and should have some leverage, so it might not actually fit on the given graph. (Feel free to send a picture via Remind if you want me to take a look). 
• 9.) A residual of -2.7 has a unit of beats per minute; this residual means that we overestimated John's pulse rate for a speed of 5 mph by 2.7 bpm.
• Extra Question: What would the actual walking speed be?
• Predicted = 63.457 + 16.2809(5) = 144.8615
• Residual = actual - predicted...
• - 2.7 = actual - 144.8615
• Actual pulse rate = 142.1615 bpm
• 10.) According to the model, as John's walking speed increases by 1 mph, his predicted pulse rate increases by roughly 16.2809 beats per minute.
• 11.) According to the data, if John's walking speed is 0 mph (John is standing still), his predicted pulse rate is about 63.457 beats per minute. (This is realistic, as John would still have a pulse if he isn't walking!)
• 12.) According to the model, 98.7% of the changes in John's pulse rate can be explained by changes in his walking speed. 

Grading Criteria: AP Free Response Groupwork

• 2007 (Form B) Problem (Heights of Fathers and Daughters)
• Section 1: Graphical Portion
• To get essentially correct the line had to be correctly drawn AND the residual is correctly drawn
• One of these two components = P
• Section 2: Calculation of Residual
• Essentially correct = correct residual with work shown
• Partially correct = correct magnitude of the residual but incorrect sign (should be negative)
• Incorrect = incorrect residual or no work shown
• Section 3: Effect on slope
• Essentially correct: student states the slope will remain about the same (or decrease very slightly) and explains based on the new point fitting the original pattern or falling close to the LSRL (low residual)
• *If student says "slope decreases" this is incorrect
• Partially correct: student states slope will remain about the same but explanation is weak/unclear
• Section 4: Effect on correlation
• Essentially correct: states new correlation will increase and explains based on the new point fitting the original pattern AND having high leverage
• Partially correct: correlation increases with an explanation that is...
• "Point is close to the line/low residual"
• Or has one of the two (point fits original pattern, has high leverage)
• For each section E = +1 point, P = +0.5 points
• 2012 Problem (Sewing Machines)
• Part A: 
• Essentially correct: student correctly describes shape (curved), direction (positive), strength (weak/moderately weak/somewhat weak), and does so in context
• Partially correct: student does 3 of the 4 things listed for E
• Part B:
• Essentially correct: correct estimation of the point (2200, 65) AND explains that the shape of the scatterplot is curved with this point (and would appear roughly linear without it)
• Partially correct: correct value of point and explanation =....
• point is an outlier
• removal of the point makes pattern more linear
• point does not follow the pattern of the others
• "High residual, high leverage"
• Part C:
• Essentially correct = circles the 2 correct points
• Partially correct = correct two points AND one ore two additional points are circled, OR one of two correct points is circled and at most one additional point is circled

Want some more practice? Try these problems in the book (and check your answers)

• Page 245: 1, 11abcd, 17, 27

• Check your answers in the back of the book! (under Part II Review)