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Chapter 12: Q4E (page 722)

Question: Suppose you fit the first-order multiple regression model y=尾0+尾1x1+尾2x2+蔚 to n=25 data points and obtain the prediction equationy^=6.4+3.1x1+0.92x2 . The estimated standard deviations of the sampling distributions of 尾1 and 尾2are 2.3 and .27, respectively

Short Answer

Expert verified

(a) Do not reject the null hypothesis, hence the value of 尾1=0

(b) Reject the null hypothesis at 95% significance level, thus, the value of 尾2=0

(c) 90% confidence interval for 尾1 is (0.0732, 6.1268).

(d) 99% confidence interval for 尾2 is (0.16751, 1.67249).

Step by step solution

01

Step-by-Step Solution  Step 1: Testing the significance β1

02

Testing the significance of  β2

Therefore, value of 尾2鈮�0

03

Confidence interval for β1

90% confidence interval for尾1is 尾^2卤t0.005蝉尾2

Therefore, the confidence interval is 3.1卤1.316脳2.3

Thus, confidence interval for尾1is (0.0732, 6.1268). Here, with 90% accuracy it can be concluded that the value of尾1will lie between 0.0732 and 6.1268. The value of also falls in the intervals which is a positive sign.

04

Confidence interval for  β2

99% confidence interval for尾2is尾^2卤t0.005蝉尾2尾^2卤t0.005蝉尾2

Therefore, the confidence interval is 0.92卤2.787脳0.27

Thus, confidence interval for 尾2 is (0.16751, 1.67249). Here, with 99% accuracy it can be concluded that the value of 尾2will lie between 0.16751 and 1.67249. The value of 尾^2 also falls in the intervals which is a positive sign

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Most popular questions from this chapter

Question: After-death album sales. When a popular music artist dies, sales of the artist鈥檚 albums often increase dramatically. A study of the effect of after-death publicity on album sales was published in Marketing Letters (March 2016). The following data were collected weekly for each of 446 albums of artists who died a natural death: album publicity (measured as the total number of printed articles in which the album was mentioned at least once during the week), artist death status (before or after death), and album sales (dollars). Suppose you want to use the data to model weekly album sales (y) as a function of album publicity and artist death status. Do you recommend using stepwise regression to find the 鈥渂est鈥� model for predicting y? Explain. If not, outline a strategy for finding the best model.

Question: There are six independent variables, x1, x2, x3, x4, x5, and x6, that might be useful in predicting a response y. A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The software fits all possible one-variable models of the form

where xi is the ith independent variable, i = 1, 2, 鈥�, 6. The information in the table is provided from the computer printout.

E(Y)=尾0+尾1xi

a. Which independent variable is declared the best one variable predictor of y? Explain.

b. Would this variable be included in the model at this stage? Explain.

c. Describe the next phase that a stepwise procedure would execute.

Question: The Excel printout below resulted from fitting the following model to n = 15 data points: y=尾0+尾1x1+尾2x2+蔚

Where,

x1=(1iflevel20ifnot)x2=(1iflevel30ifnot)

Can money spent on gifts buy love? Refer to the Journal of Experimental Social Psychology (Vol. 45, 2009) study of whether buying gifts truly buys love, Exercise 9.9 (p. 529). Recall those study participants were randomly assigned to play the role of gift-giver or gift-receiver. Gift-receivers were asked to provide the level of appreciation (measured on a 7-point scale where 1 = 鈥渘ot at all鈥� and 7 = 鈥渢o a great extent鈥�) they had for the last birthday gift they received from a loved one. Gift-givers were asked to recall the last birthday gift they gave to a loved one and to provide the level of appreciation the loved one had for the gift.

  1. Write a dummy variable regression model that will allow the researchers to compare the average level of appreciation for birthday gift-giverswith the average for birthday gift-receivers.
  2. Express each of the model鈥檚 尾 parameters in terms ofand.
  3. The researchers hypothesize that the average level of appreciation is higher for birthday gift-givers than for birthday gift-receivers. Explain how to test this hypothesis using the regression model.

Question:How is the number of degrees of freedom available for estimating 蟽2(the variance of蔚 ) related to the number of independent variables in a regression model?
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