Mr. Rogers  AP Statistics Objectives

AP Statistics Super Splendid Non Linear Regression Practice Test  
1  )  A common response variable influences __________________. both the x and y or response and explanatory variables  
2  )  Residuals can be mathematically defined as follows: resid = y_{i } yhat  
3  )  When a power regression is performed, which variable(s) is/are transformed? Both are transformed. The y or response variable is transformed into Ln (y) and the x or explanatory variable is transformed into Ln (x).  
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. No, there could be a nonlinear association  
6  )  Write the official Statistics definition of slope. For every increase of one in the xvariable, the predicted y increases by the slope  
7  )  For a least squares regression, If Sx = 8, r^2 = 0.64, and the slope = 100, what does Sy equal? Sy = 1000  
8  )  Which is smaller SST or SSE? Usually SSE but they could be equal if Rsquare = 0  
9  )  Name a situation where an exponential regression would likely be appropriate. Growth/decay.  
10  )  When an exponential regression is performed, which variable(s) is/are transformed? The y or response variable is transformed into Ln (y)  
11  )  Why is a high level of association based on a single regression analysis not be considered proof of causation? Lurking variables or random events may be responsible for the association.  
12  )  For a regression/correlation analysis Rsquare = 0.75. Using the definition of Rsquare, explain what the number means. The regression equation explains 75% of the variability in the ydata.  
13  )  What is the first thing that should be done when performing regression analysis. Scatter plot  
14  )  If a residual plot has a pattern in it what conclusion should you draw about the regression equation? It's inappropriate  
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21  )  For a least squares regression, yhat = 4x + 20, r^2 = 0.64, Sy = 5, xbar = 20. Find ybar. ybar = 100  
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. 40  
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. 48  
24  )  State the pitfall of using averaged data rsquare becomes closer to 1.0, the association appears stronger than it rally is.  
25  )  What is a confounding variable? affects only ydata  
26  )  What is a common response variable? affects xdata and ydata  
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  
linear equation analysis



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