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Chapter 12: Q27E (page 732)

Question: Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the impact of reality TV shows on one’s desire to undergo cosmetic surgery, Exercise 12.17 (p. 725). Recall that psychologists used multiple regression to model desire to have cosmetic surgery (y) as a function of gender(x1) , self-esteem(x2) , body satisfaction(x3) , and impression of reality TV (x4). The SPSS printout below shows a confidence interval for E(y) for each of the first five students in the study.

  1. Interpret the confidence interval for E(y) for student 1.
  2. Interpret the confidence interval for E(y) for student 4

Short Answer

Expert verified

(a) The confidence interval for E(y) for student 1 here is (13.42, 14.31) which can be interpreted as the population mean or average desire to have cosmetic surgery will be between the interval (13.42, 14.31) for student 1.

(b) The confidence interval for E(y) for student 4 here is (8.79, 10.89) which can be interpreted as the population mean or average desire to have cosmetic surgery will be between the interval (8.79, 10.89) for student 4.

Step by step solution

01

Step-by-Step SolutionStep 1: Interpretation of confidence interval for the population mean

Student 1’s desire to have cosmetic surgery can be computed at 11. The confidence interval for E(y) for student 1 here is (13.42, 14.31) which can be interpreted as the population mean or average desire to have cosmetic surgery will be between the interval (13.42, 14.31) for student 1.

02

Explanation of confidence interval for the population mean

Student 4’s desire to have cosmetic surgery is represented as 11. The confidence interval for E(y) for student 4 here is (8.79, 10.89) which can be interpreted as the population mean or average desire to have cosmetic surgery will be between the interval (8.79, 10.89) for student 4

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Most popular questions from this chapter

Question:Suppose you fit the first-order model y=β0+β1x1+β2x2+β3x3+β4x4+β5x5+εto n=30 data points and obtain SSE = 0.33 and R2=0.92

(A) Do the values of SSE and R2suggest that the model provides a good fit to the data? Explain.

(B) Is the model of any use in predicting Y ? Test the null hypothesis H0:β1=β2=β3=β4=β5=0 against the alternative hypothesis {H}at least one of the parameters β1,β2,...,β5 is non zero.Useα=0.05 .

Question: Diet of ducks bred for broiling. Corn is high in starch content; consequently, it is considered excellent feed for domestic chickens. Does corn possess the same potential in feeding ducks bred for broiling? This was the subject of research published in Animal Feed Science and Technology (April 2010). The objective of the study was to establish a prediction model for the true metabolizable energy (TME) of corn regurgitated from ducks. The researchers considered 11 potential predictors of TME: dry matter (DM), crude protein (CP), ether extract (EE), ash (ASH), crude fiber (CF), neutral detergent fiber (NDF), acid detergent fiber (ADF), gross energy (GE), amylose (AM), amylopectin (AP), and amylopectin/amylose (AMAP). Stepwise regression was used to find the best subset of predictors. The final stepwise model yielded the following results:

TME^=7.70+2.14(AMAP)+0.16(NDF), R2 = 0.988, s = .07, Global F p-value = .001

a. Determine the number of t-tests performed in step 1 of the stepwise regression.

b. Determine the number of t-tests performed in step 2 of the stepwise regression.

c. Give a full interpretation of the final stepwise model regression results.

d. Explain why it is dangerous to use the final stepwise model as the “best” model for predicting TME.

e. Using the independent variables selected by the stepwise routine, write a complete second-order model for TME.

f. Refer to part e. How would you determine if the terms in the model that allow for curvature are statistically useful for predicting TME?

Question: Determine which pairs of the following models are “nested” models. For each pair of nested models, identify the complete and reduced model.

a.E(y)=β0+β1x1+β2x2b.E(y)=β0+β1x1c.E(y)=β0+β1x1+β2x12d.E(y)=β0+β1x1+β2x2+β3x1x2e.E(y)=β0+β1x1+β2x2+β3x1x2+β4x21+β5x22

Question: Failure times of silicon wafer microchips. Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer-Level Packaging Conference, November 3–4, 2005). The failure times of the microchips (in hours) were determined at different solder temperatures (degrees Celsius). The data for one experiment are given in the table. The researchers want to predict failure time (y) based on solder temperature (x).

  1. Construct a scatterplot for the data. What type of relationship, linear or curvilinear, appears to exist between failure time and solder temperature?
  2. Fit the model,E(y)=β0+β1x+β2x2, to the data. Give the least-squares prediction equation.
  3. Conduct a test to determine if there is upward curvature in the relationship between failure time and solder temperature. (use.α=0.05)

Question: Consider the model:

y=β0+β1x1+β2x2+β3x3+ε

where x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding scheme

role="math" localid="1649846492724" x2=1   iflevel 20  otherwise       x3=1   if level 30   otherwise

The resulting least squares prediction equation is y^=44.8+2.2x1+9.4x2+15.6x3

a. What is the response line (equation) for E(y) when x2 = x3 = 0? When x2 = 1 and x3 = 0? When x2 = 0 and x3 = 1?

b. What is the least squares prediction equation associated with level 1? Level 2? Level 3? Plot these on the same graph.
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