Mr. Rogers  AP Statistics Objectives

AP Statistics Super Splendid Non Linear Regression Practice Test  
1  )  A common response variable influences __________________.  
2  )  Residuals can be mathematically defined as follows:  
3  )  When a power regression is performed, which variable(s) is/are transformed?  
4  )  Name 4 ways to establish causation  
5  )  Bob looks at a regression analysis with an rsquare of 0.11, a slope of .17, and an intercept of 6, and concludes that there is definitely no relationship between the variables. Is this a proper conclusion? Explain.  
6  )  Write the official Statistics definition of slope.  
7  )  For a least squares regression, If Sx = 8, r^2 = 0.64, and the slope = 100, what does Sy equal?  
8  )  Which is smaller SST or SSE?  
9  )  Name a situation where an exponential regression would likely be appropriate  
10  )  When an exponential regression is performed, which variable(s) is/are transformed?  
11  )  Why is a high level of association based on a single regression analysis not be considered proof of causation?  
12  )  For a regression/correlation analysis Rsquare = 0.75. Using the definition of Rsquare, explain what the number means.  
13  )  What is the first thing that should be done when performing regression analysis.  
14  )  If a residual plot has a pattern in it what conclusion should you draw about the regression equation?  
15  )  Convert the following into an exponential form: ln(yhat) = 5x + 7  
16  )  Convert the following into an exponential form: ln(yhat) =  2x + 4  
17  Convert the following into a power equation form: ln(yhat) =  4(lnx) + 2.75  
18  )  Convert the following into a power equation form: ln(yhat) = 3(lnx) + 5  
19  )  For a least squares regression, If Sx = 12, r^2 = 0.8 and Sy = 4 equal what is the slope equal to?  
20  )  For a least squares regression, yhat = 4x + 20, r^2 = 0.64, Sy = 5. What is Sx?  
21  )  For a least squares regression, yhat = 4x + 20, r^2 = 0.64, Sy = 5, xbar = 20. Find ybar.  
22  )  For a least squares regression, yhat = 4x + 20, r^2 = 0.64, Sy = 5, xbar = 20. x is increased by 10. Find the corresponding increase in y.  
23  )  For a least squares regression, yhat = 4x + 20, r^2 = 0.64, Sy = 5, xbar = 20. Find the value of y when x = 7  
24  )  State the pitfall of using averaged data  
25 
)  What is a confounding variable?  
26  )  What is a common response variable?  
27  )  Bob decides to sell bacteria burgers for a living. (They're full of protein and easily grown.) He has heard of linear regression and wants a linear model. Perform linear regression for him and report the results. Explain why this is not a good model. Next perform an appropriate form of nonlinear regression and explain this model to him. Make sketches of the scatter diagram for the data and all residual plots. Do not forget to report and explain the rsquare values.  
time: 1  2  3  4  5  6  7  8  
number of bacteria: 2  5,  9  19  30  68  130  252 
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