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Chapter 12: Q8E (page 722)

Question:If the analysis of variance F-test leads to the conclusion that at least one of the model parameters is nonzero, can you conclude that the model is the best predictor for the dependent variable ? Can you conclude that all of the terms in the model are important for predicting ? What is the appropriate conclusion?

Short Answer

Expert verified

It cannot be concluded if a model parameter is a best predictor for model or it can be concluded if all the term in the model is important just on the basis of F-test.

Step by step solution

01

Step-by-Step Solution Step 1: Best predictor for the dependent variable

It cannot be concluded if a model is the best predictor for the dependent variable y because the F-test leads to the conclusion that at least one of the model parameters is nonzero since it does not compare this model to other models which can be fitted to the data.

02

Overall goodness of the fit

Similarly, it cannot concluded that all the terms in the model are important in predicting just through the F-test because we only know one of the parameters is zero but we do not know if all the parameters are zero.

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Most popular questions from this chapter

Question: Failure times of silicon wafer microchips. Refer to the National Semiconductor study of manufactured silicon wafer integrated circuit chips, Exercise 12.63 (p. 749). Recall that the failure times of the microchips (in hours) was determined at different solder temperatures (degrees Celsius). The data are repeated in the table below.

  1. Fit the straight-line modelEy=β0+β1xto the data, where y = failure time and x = solder temperature.

  2. Compute the residual for a microchip manufactured at a temperature of 149°C.

  3. Plot the residuals against solder temperature (x). Do you detect a trend?

  4. In Exercise 12.63c, you determined that failure time (y) and solder temperature (x) were curvilinearly related. Does the residual plot, part c, support this conclusion?

Question: Suppose you fit the interaction model y=β0+β1x1+β2x2+β3x1x2+ε to n = 32 data points and obtain the following results:SSyy=479, SSE=21, β^3=10, and sβ^3=4

a. Find R2and interpret its value.

b. Is the model adequate for predicting y? Test at α=.05

c. Use a graph to explain the contribution of the x1 , x2 term to the model.

d. Is there evidence that x1and x2 interact? Test at α=.05 .

Minitab was used to fit the complete second-order modeE(y)=β0+β1x1+β2x2+β3x1x2+β4x12+β5x22to n = 39 data points. The printout is shown on the next page.

a. Is there sufficient evidence to indicate that at least one of the parameters—β1,β2,β3,β4, andβ1,β2,β3,β4—is nonzero? Test usingα=0.05.

b. TestH0:β4=0againstHa:β4≠0. Useα=0.01.

c. TestH0:β5=0againstHa:β5≠0. Useα=0.01.

d. Use graphs to explain the consequences of the tests in parts b and c.

Question: Bordeaux wine sold at auction. The uncertainty of the weather during the growing season, the phenomenon that wine tastes better with age, and the fact that some vineyards produce better wines than others encourage speculation concerning the value of a case of wine produced by a certain vineyard during a certain year (or vintage). The publishers of a newsletter titled Liquid Assets: The International Guide to Fine Wine discussed a multiple regression approach to predicting the London auction price of red Bordeaux wine. The natural logarithm of the price y (in dollars) of a case containing a dozen bottles of red wine was modelled as a function of weather during growing season and age of vintage. Consider the multiple regression results for hypothetical data collected for 30 vintages (years) shown below.

  1. Conduct a t-test (atα=0.05 ) for each of the βparameters in the model. Interpret the results.
  2. When the natural log of y is used as a dependent variable, the antilogarithm of a b coefficient minus 1—that is ebi - 1—represents the percentage change in y for every 1-unit increase in the associated x-value. Use this information to interpret each of the b estimates.
  3. Interpret the values of R2and s. Do you recommend using the model for predicting Bordeaux wine prices? Explain

Suppose the mean value E(y) of a response y is related to the quantitative independent variables x1and x2

E(y)=2+x1-3x2-x1x2

a) Identify and interpret the slope forx2

b) Plot the linear relationship between E(y) andx2for role="math" localid="1649796003444" x1=0,1,2, whererole="math" localid="1649796025582" 1≤x2≤3

c) How would you interpret the estimated slopes?

d) Use the lines you plotted in part b to determine the changes in E(y) for eachrole="math" localid="1649796051071" x1=0,1,2.

e) Use your graph from part b to determine how much E(y) changes whenrole="math" localid="1649796075921" 3≤x1≤5androle="math" localid="1649796084395" 1≤x2≤3.
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