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Practice Problems # 12 - Solutions
1. The following table gives values for hypothetical variables x and y.
x y x y 1.0 2.2 11.0 31. 2.0 9.0 12.0 32. 3.0 13.5 13.0 34. 4.0 17.0 14.0 36. 5.0 20.5 15.0 37. 6.0 23.3 16.0 38. 7.0 25.2 17.0 40. 8.0 26.4 18.0 41. 9.0 27.6 19.0 42. 10.0 30.2 20.0 43.
a. Create a scatter plot of y versus x.
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Scatter Plot of x vs. y
x
y
b. Fit a simple linear regression model to this data.
Estimated Model 8.65263157894737+ 1.91022556390977x*
c. Using the model in part b, create a residual plot of the residuals vs. x.
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Residuals of y vs. x
x
Residuals of y
d. Create a residual plot of the residuals vs. fitted values.
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Residuals of y vs Predicted
Predicted y
Residuals of y
d. Do these plots indicate an adequate fit? Explain. No, they do not indicate an adequate fit to the data. There is a definite pattern in the residual plots; hence we should use a polynomial regression model in the variable x (i.e. at the very least, one should include x^2 and well as x in the regression model; maybe even cubic).
